Going through

In fairness, Hypnos filed at 2:30am on the date he was eligible, not a few minutes after midnight.   Is it early in the morning?  Sure, but it's his prerogative.
 
If the priority date is set the day before---even if he filed at 8am that still could have happened in his case.  With my own application, I filed at 7pm in the evening and my priority date was still set a day behind....I would have been in the same situation as OP is now if I'd applied on the very day I became eligible.
 
I'm sure Hypnos wishes he'd waited a day or two before submitting the N400...I'm sure he also wishes that USCIS set his priority date by the date the application was actually submitted, as they should be doing.

USIC's website provides some great tips on fasteners, binders etc. and how they prefer your package to be assembled.  In part it reads:
 
In preparing your packet, remember: Do not use binders or folders that we cannot easily disassemble. Use fasteners to hold together thick or bulky applications or petitions. Two-hole punching the top of the material for easy placement in the file is appreciated. Sticky tabs assist in locating items listed as attachments. For easy filing, place the tabs on the bottom of the page, not the side. Do not use heavy-duty staples; instead use fasteners or heavy clips. Do not submit originals unless specifically required.  Do not submit oversized documentation unless it is necessary. If you are sending more than one case in an envelope, clearly separate the cases by rubber band or fasteners.  
https://www.uscis.gov/forms-filing-tips 

Lots of good information in this thread---no real need for the N600 especially if the child already has a US passport...
 
If you've got $1,170 to spare on a piece of paper your child doesn't need since they have proof of citizenship already....suppose no one can tell you how to spend your money.
 
Naturally USCIS is happy to take your money at any time.

Ok.  You seem determined to travel then because you don't want to lose money on the wedding "celebration" (since you are already married).  
 
I'm normally not this blunt---I think most who know me on these forums will attest to that.  I will be blunt with you now, based on my experience with helping others in your situation, my own experiences, and based on what I know happens at the border when certain criminal charges are at play:
 
In effect, you are hanging her out to dry:
 
-she is not guaranteed re entry into the US, despite having a pending AOS application.
-she is not guaranteed re entry into the US, despite having an approved Advanced Parole.
-she is not guaranteed re entry into the US, despite travelling back with a USC husband.
-she is not guaranteed re entry into the US, despite having been scheduled to appear in a US court house.
-she can be denied re entry due to her open charge of Domestic Violence (POE won't care if you say you are dropping the charges later on---they care about what's right in front of them at that moment).
-not having any documents to show regarding the arrest/final disposition will heighten the chances of her being denied re entry.  DV by impending immigrants is taken quite seriously at the border.  
-her passport/scanned fingerprints/name will come up as a "hit" at the border, showing there was a recent arrest on the officer's computer but not much more details than that.  Her getting a "hit" can commonly result in her being sent to secondary inspection--without you--where she will have to explain herself and her charges.  Without any official paperwork to show (since you are determined to travel before her court appearance), she is going to be put through the wringer.   
-if/when she is denied entry you will have to come up with a Plan B if you wish to continue to live together in the same country.
 
She is a non-citizen.  She is not even a LPR at this stage.  Do not be flippant about her travelling---because this is not a game she can afford to lose.
 
YOU, however, need to weigh all of the above against the monetary loss you will incur by postponing your party plans.
 
 
 
 

Since she has the 10-year greencard, she can apply for citizenship when eligible (or afterwards when the marital status would be irrelevant to the N400)
She won't need your consent, authorization or even your participation to become a citizen if she wished.
 
Cheating on a spouse does not equal entering the marriage under false pretenses.  
That being said, if you have concrete evidence that she committed immigration fraud (love letters are not going to be enough here), you can certainly report your findings.
 
 

Well...she's got 90 days to marry you, or else legally she needs to return to her home country.
Whatever you do, do NOT find yourself pressured into marrying her and "working things out" later or something like that, if that's her plan---will just make everything more complicated for you in the end with divorce/financials/etc.
 
I understand the thought behind paying for the plane ticket/short hotel stay----but 2 months wages??  To me, that's just opening the door for her to potentially milk you out of more money on an ongoing basis because you feel guilty over what's happened.
 
There's also the issue of how will you make sure she gets on the plane?  

Do not get married in Columbia...the purpose of the K1 is for your fiance to marry you in the United States, not another country. 
If you get married in Columbia first, you will cause problems for yourself once you reach the AOS stage/interview...and is very easily found out once they compare the date of your marriage certificate to the date of entry under the K1.

I've seen some people on VJ "forget" they had children when filling out forms....

In Russia it is tradition for the patronymic name to appear on the birth certificate and foreign passport.  The OP has not done anything illegal by not using that name on other documents.  He does not need any sort of "legal name change document" in his situation, as he has never changed his legal name.
 
OP, if your concern is that your patronymic name will appear on documents after your oath ceremony, when you apply for your US passport there is an option on the application to include only your first and last name.  Once you get your US passport, then use that document to update your SS, drivers license, etc.   Your US passport is sufficient for proving your citizenship going forward.  You don't need to worry about the green card, because you turn that in during your oath ceremony where they destroy it since you no longer need a GC after becoming a citizen.
 
If they question this at the passport office when applying (they most likely will not), you can show through all of your other US identification that you have been using only your first and last name consistently (not your patronymic name) on all of your other legal documents.
 
Your naturalization certificate is not needed for anything other than submitting with your passport application, and for proving your citizenship should you wish to sponsor family members in the future.  So just tuck it safely into a strongbox somewhere and then forget about it.  

If the person leaves before AP is approved, the AOS can be deemed as abandoned and the person may have issues reentering the US.
Leaving the US while going through AOS, and the AP is still pending is not advised. 
 
 

Some people are in more of a "rush", or "keep track to the minute" to get citizenship due to a job offer/career plans that entail being a citizen to be eligible for it, as one example.

I know of countries where such things as machismo attitudes abound...where the man is the head of the household, and the woman is generally the subservient, etc. 
 
I know of no countries where threatening a spouse with a knife is a common occurrence in everyday marriage.
 
My parents came from a country where domestic violence laws weren't even created until the early 1980s.
 
As for the part of your post about making amends and the violent spouse learning their lesson through counselling, and whether members agree with that stance?---
 
I believe in forgiveness, and I believe that people can change certain behaviours.  But I also believe that there are other certain behaviors which are prone to escalate, not diminish, over time.
 
Call me harsh, but as much as I can love a person?  Even the father of my children?  There's no going back from that.  And I'm not putting myself---or any children---in a situation where it might happen again, or worse.  No promises in the world from someone who did that to me once is going to make me believe something won't happen again.  This time she was lucky.  Next time he might fly in a rage and beat her up.  Next time his mind may be in a place where she won't even see it coming and he slits her throat while she's sleeping.  
 
It only takes one time for someone to threaten me with a knife for me to realize the relationship is over completely.  But that's just my view on it.
 

I just wanted to say that I enjoyed my time in this group, wish those whose threads I became involved in the best of luck in their own visa journey---and will miss a lot of members here whom I very much respect and enjoyed interacting with like @geowrian @TBoneTX @mindthegap @Boiler @Jorgedig @Villanelle @NikLR and so many others whose usernames are slipping from my memory now.   Being a member here also filled a "social hole" for me, and while it's difficult to leave it's something I need to do.  I hope I have helped others along the way where needed.

There's no way for me to leave any sort of "contact info" without it being (rightfully) edited out by Admin for posting personal info---or else I would just to be able to keep in touch with anyone who wished to.  

Ah well...off to figure out how to close my account now (I know that button is around here somewhere lol)

Take care all. 

Assure them of....what...exactly?  That they may or may not stand the possibility of being picked up and deported?  That they may or may not have to look over their shoulders for years in fear of that?  That they may or may not ever have to travel to their home country for emergency purposes and then be trapped with no legal basis to return?  That they may or may not have to work illegally to help support their family later on?
 
Like you said, everybody's situation is different.  It worked out for your wife in the end, the next person may not be as lucky.

Remember to, when filing online, you can print out the snapshot of your e-file (log into the case activity uscis website to download it)...that way when you go to your interview, you can prove exactly what you uploaded with your application if there's ever a question of "you didn't submit this when you filed."  All of the evidence uploads show on the last page.

The question is more referring to if you had an online account number BEFORE filing this application online.
Since you've never filed an application online before now, you are fine with leaving that section blank.

You sound like me  
 
I've been living here since 2004 and I still do not have one person "in real life" in this country that I can call a "friend".  VJ has become the stand-in for any sort of social life, which is the main reason why I've still stuck around the forums after naturalizing.
 
I also vote for sticking it out.  It's not as long as you may think----put it this way, you've come this far already in your immigration journey...another 3 years will fly by in comparison even though it doesn't feel that way now.  The main benefit being you can come and go as you please afterwards.  The main drawback being that you have to file US taxes for the rest of your life no matter where you live.
 
 
 

To show that you weren't charged for the replacement since it was a DHS error.  As for why 2 separate receipts, might be a clerical error/duplicate receipt sent out, might be that this is how they issue the i-90 receipt now---one showing submission of the application, one showing any billing details.
 
Either way doesn't affect anything, if just another receipt notice sent, nothing to stress out about.

According to USCIS, and the instructions plainly written, the original is required at the time of your application:
 
Item Number 2.d. My existing card has incorrect data because of Department of Homeland Security error. Select this reason if your card has incorrect data and the error was caused by DHS. Attach the original Permanent Resident Card issued with the incorrect data. A copy of the card is not acceptable in this case.
 
I would allow up to at least 3 weeks to receive the receipt notice (or more likely in your case, a RFE for the original card).

It's good that you notified them already---yes, it will have to be resealed.
 
On the plus side, you didn't slice through any of the documents inside, as well.

I remember a thread where someone wanted to send bloody sheets as proof of the bride being a virgin and the marriage consummated. 

About half a year after I was authorized to work----and only because of a connection my husband had through a friend.  I purposefully took the first six months "off" to fix up the home, get settled, explore the city, that sort of thing.

I just wanted to say that I enjoyed my time in this group, wish those whose threads I became involved in the best of luck in their own visa journey---and will miss a lot of members here whom I very much respect and enjoyed interacting with like @geowrian @TBoneTX @mindthegap @Boiler @Jorgedig @Villanelle @NikLR and so many others whose usernames are slipping from my memory now.   Being a member here also filled a "social hole" for me, and while it's difficult to leave it's something I need to do.  I hope I have helped others along the way where needed.

There's no way for me to leave any sort of "contact info" without it being (rightfully) edited out by Admin for posting personal info---or else I would just to be able to keep in touch with anyone who wished to.  

Ah well...off to figure out how to close my account now (I know that button is around here somewhere lol)

Take care all. 

In all fairness, she's got somewhat of a gun held to her head...so hard to think out a solution with that sometimes.
 
She has an ex husband who (either in her head, or in reality) somewhat hopes her i-751 is denied, and that then she is deported without her child.  
 
If she gets deported then she cannot enter the US for quite a period to see her child.  And she cannot guarantee you will send the child to the Ukraine--like you said you will fight with everything you've got to prevent visitation to her as well--perhaps even going so far as to mention something along those lines to her, which would stick in her head naturally.  What other option are you giving her, then?  If she cannot enter the US, obviously there's only one other solution I can think of to her exercising her visitation rights.  
 
She's also living in the same house as her ex husband as a constant reminder of these things, and under quite a bit of pressure along with normal pressure of being a new mother caring for a baby.  It's a shame she can't get her own physical space in this---might be a bit easier to be able to sort her head out and then try to come up with workable solutions with some distance between you two.  Might be better for you, too.

Are you sure they were asking for photos from your previous marriage....or photos from your current marriage when the wedding took place?  Seems strange they would want wedding photos with ex spouses...  I'm wondering if it was a misunderstanding since she was using an interpreter?
 
Perhaps her family members would have held on to some of those old photos?