Just Paul

To be eligible he would have had to spend 5 years in the US prior to the birth of the child(ren) as a citizen.  Two of those since the age he was 14.
 
There is no need for him to be in the US right now for CRBA.

Congrats!!!!

what @John & Rose mentioned is 100% true.  His K1 was denied. K1's are not appealable.  He ended up getting married and started the spousal visa which takes longer time.
 
If time is more important you might want to get married because of the criminal issue.   If the petition comes up for denial it can be reaffirmed by USCIS and sent back to the Consulate. 
 
If you do the K1 it might be outright denied.  It can be denied at the USCIS or the DOS.  If it is denied by DOS you can not seek a waiver.   
 
You don't state how old the adult charges are.   The more seasoned they are the less of an overall impact they can have.

Very true...
 
A K-1 is more likely to be ultimately denied than a CR-1.
A refused K-1 with the petition being sent back will sit and die.
A refused CR-1/IR-1 with the petition being sent back can be reaffirmed and not refused again for the same reason if based upon the same evidence.

You can at least appeal a spousal denial.

Well we see you have already started the planning of your I-864.     I would wait until you get your NOA2 before proceeding with police reports as they are only good for a year. He will need police reports for both Nigeria and Turkey. 

I would highly recommend writing cover letters/table of contents for EACH form, not just the entire package.
The reason? The forms are not processed as a package and are shipped to different offices eventually. Once the I765 and I131are removed from the package and sent to their adjudicator, they will no longer have the "package" cover letter attached. If by chance the adjudicator loses a part of your form's documents they can alway look to the cover letter for each form to see that you did indeed send what they are looking for and will know to search for it if in fact it is on their desk somewhere. If it did not have a cover letter they could just assume you did not send it and send you and RFE/RFIE.

So, short answer is no she wasn't alone. I went with her and I got asked questions too.  
 
Long answer - We were Third Country National DCF in CDMX.  There they don't allow the Petitioner in.  But she did the interview and they asked if I was there because the CO had some questions she could not answer about my finances.   I went back with her and did the interview.  Fortunately I was there because then the CO then said there was an issue with her police clearance for Mexico.  Which there was not.   
 
If you can be there, afford to be there, it will set her at ease.   Last April in Manila when she was getting ready to leave to join me in Mexico I was there with her too.  It was good to be there to help her wind up things like close her bank account, get her international driving permit and pack her things.   I left a few days before her because I had meetings in the states.  I took a bunch of her things with me and then picked her up in Tijuana.
 

We have a 27 year difference.  After a year we married on 4th trip.  
 
We did lots of practice questions.  She was very prepared.

Yes,  but the interviews are very very similar.   The most common issues are: is the beneficiary likely to become a public charge, is this a bonafide relationship?   They replace the word fiancee with spouse.  They still ask how did you meet, what does the petitioner do, where are you going to live etc?

So, short answer is no she wasn't alone. I went with her and I got asked questions too.  
 
Long answer - We were Third Country National DCF in CDMX.  There they don't allow the Petitioner in.  But she did the interview and they asked if I was there because the CO had some questions she could not answer about my finances.   I went back with her and did the interview.  Fortunately I was there because then the CO then said there was an issue with her police clearance for Mexico.  Which there was not.   
 
If you can be there, afford to be there, it will set her at ease.   Last April in Manila when she was getting ready to leave to join me in Mexico I was there with her too.  It was good to be there to help her wind up things like close her bank account, get her international driving permit and pack her things.   I left a few days before her because I had meetings in the states.  I took a bunch of her things with me and then picked her up in Tijuana.
 

We have a 27 year difference.  After a year we married on 4th trip.  
 
We did lots of practice questions.  She was very prepared.

Rentals & 401k?   Fill out the asset section and you might, or also, qualify that way.

Yes 3

I had a friend in a similar circumstance to yours.   Domestic Violence / AWA.  Charged and pled down from a felony.  He was able to get an I-130 for a CR-1 approved without RFE.  Like others said be very truthful on the filing.  Ultimately USCIS/ DOS will want either certified copies of the disposition (sentencing) or a certified copy of no records found.   
 
For a K1 you have to get a waiver.   No waiver for a CR1.
 
I would order a copy of your FBI report to make sure everything is ok and to know what they are going to see.  It is possible to see things not on the report but it is good to run your own to make sure there isn't anything inaccurate or even a surprise.
 
Your spouse will need to know about all of the charges.  Expect it to come up at the interview.
 

Capital One allows you to add a Foreign Spouse, even Girlfriend, as an authorized user.  That's what I did with Mary.  She had an US credit card before we married.  You can even do it online just enter 000-00-0001 as the SSN or call it in.   Just make a charge on it in the US before your use it internationally.

Please fill in a timeline when you get a chance . . . Under your profile page.

Just to add to the conversation:  I look for others answers.
I am using an online service to produce the documents for me, I will leave un-named.
I am for my wife and three children.
Wife's 1-864 
Part 3 -1 : Yes
Part 3-29: 1
 
Part 5-1 : 1
Part 5-2 : 1
Part 5-3: 0
Part 5-4 : 3
Part 5-5 : 0
Part 5-6 : 0
Part 5-7 : 0
Total Household : 5
 
The three children look like this on their own 1-864
Part 3 -1 : Yes
Part 3-29: 1
 
Part 5-1 : 1
Part 5-2 : 1
Part 5-3: 1
Part 5-4 : 2
Part 5-5 : 0
Part 5-6 : 0
Part 5-7 : 0
Total Household : 5
 

Our case was a little complicated (divorces, etc) and we have an age difference and we also married after knowing each other a very short time. They asked for a lot of evidence (everything from the wedding, basically any evidence you can imagine, they asked "Do you have a copy of this?") and they also asked my husband all the questions, I mostly just sat there and was instructed not to answer, my husband had to answer. It was stressful and felt a little bit like an interrogation, heh. 😓
 
I wrote about my experience a while ago. You can check it out but keep in mind, everyone's experience is different and Thailand might be different:
 
 

USCIS is part of DHS.
https://www.uscis.gov/about-us/find-uscis-office/international-offices/thailand-uscis-bangkok-field-office  Read about the I-130
It looks like they don't book appointments online.  Just walkin.
 
For frontloading ideas just enter "frontload cr1" or "frontload I130" in the search bar above.   Do what you can to make a strong initial petition.
 

You can go anywhere you want in the US.   Take your passport as there are places within 100 miles of the border when legal status is checked.

The 3 USCIS offices in America are all ones ones on military bases.
 
Many functions  at Cuba have been eliminated because if staff being "microwaved"

No she doesn't need a bank account.  Mine did set one up and it was cheaper for me to put money from the US into that account.
 
To quote my asawa "Welcome to the  Fee-lippines"

No she doesn't need a bank account.  Mine did set one up and it was cheaper for me to put money from the US into that account.
 
To quote my asawa "Welcome to the  Fee-lippines"

Use the old form until the a new form is published.  This is covered numerous times here. There is a search button on the top right of this page.