Hypnos

It is a violation. The K-1 legal status ends at the 91st day. So she is out of status until the AOS is filed, then she is in what's called "a period of authorized stay". 

It would only be a violation of rights if they were refused entry but came anyway, or if they took her involuntarily. Being permitted entry and/or being told to show up somewhere later is not a violation of rights. There’s a difference between upholding your own rights (not letting ICE inside without a valid arrest warrant, or refusing to hand over your passport) and somebody violating your rights by telling you to show up or else you could face penalties.
 
Also following this to see if it’s a one-off case or if it is part of a larger enforcement movement.

Having all the documents and actually presenting them to the ICE agents are two different things.  You said you were at work when ICE showed up, so my question was did your wife actually show the agents the documents?

It’s not unheard of ICE stopping by if the I-94 has expired and AOS was not filed yet. It is odd that they came by after AOS was filed, and that they want you to check in every month.

I had to use the passport agency to renew my passport when I had a lot of travel planned.  Very easy and smooth...just ensure you bring proof of your upcoming travel.

You still don't get it. There are two separate requirements:
 
1) Physically present for 18 months prior to the date you file. You meet this requirement.
2) Continuous residence for 3 years prior to the date you file. It is presume that continuous residence is broken with absence of more than 6 months but less than 1 year, unless the applicant can prove otherwise. This is your problem right here.
An applicant may overcome the presumption of loss of his or her continuity of residence by providing evidence to establish that the applicant did not disrupt his or her residence. The evidence may include, but is not limited to, documentation that during the absence: 
-The applicant did not terminate his or her employment in the United States or obtain employment while abroad.
-The applicant’s immediate family remained in the United States.
-The applicant retained full access to his or her United States abode.
 
So either you do that, or reapply, you should be good now. 
 
All of this could have been avoided had you waited until December to apply.

Just from my own personal experience in 2017:
 
I filed under the 5 year rule.  At the beginning of my interview, the IO requested to see my husband's US passport or my husband's US birth certificate.  I had both on me, and presented her with the US passport.  
 
I suppose it was more of a fact-checking exercise on her part, since my marital status should have been irrelevant for my filing under the 5-year residence rule, and no more questions about him were asked afterwards (except for a few brief minutes later on in the interview when I suppose she was determining my initial GC was properly approved)---even then those questions were mundane and seemed like further fact-checking against info already in my file---- such as "he still works for X company?"  "Your date of marriage was____"?
 
The US passport is proof of US citizenship, so should suffice.

Ok, so you were obligated to register with Selective Service the day you fell out of a lawful nonimmigrant status, which occurred on 19th July, 2014. And then once you turned 26 on 4th September, 2014 it was too late for you to register, since once you turn 26 you can no longer register with Selective Service. Unfortunately you were expected to register during those six weeks or so. And that kindof blows, but there it is.
 
So on the N-400 you would be required to answer Yes to the Selective Service question (that you were required to register but failed to do so). Now, if you send in your N-400 after turning 31 then you're not meant to need a status information letter from Selective Service... but honestly I would go ahead and get one anyway, because I know from personal experience it can take several weeks to receive it, and you'll be slightly screwed if USCIS ask for it and you don't have it on hand. 
 
To get a status letter you simply complete the following form and mail it in to Selective Service: https://www.sss.gov/Portals/0/PDFs/Status.pdf
 
As you say, if you apply once you turn 31 then your failure to register falls outside of the five year "good conduct" period and will not prevent your naturalisation.
 
There is an outside chance that you were automatically registered through your entry on a K-1. I don't think that happens; I believe only sending in an I-485 makes USCIS register you, but it never hurts to ask. So before requesting a status information letter I would call Selective Service tomorrow at 1-888-655-1825 and ask them to double check their records to see if you are registered or not. I assume you've already tried searching for yourself on their site and not found anything. Their phone agents have the ability to do a more thorough search of their systems than you or I mere mortals do.
 
If they verify that you aren't registered, then go ahead and send in the completed pdf to get a copy of your status letter, and file your N-400 once you have turned 31. It should no longer be an issue.
 
I also failed to register, and even though I am slightly older than 31 I still submitted a copy of my status letter with my application. At my interview she asked me to confirm that I didn't register, and I stated I hadn't. I pointed out that I had included a copy of my status letter, and then she saw it. And that was that.

There is no set time limit, just however long CBP grants at the border. Usually this is 6 months, but not always. There's no way to know how long it will be until you enter.
It is possible to do your plan of visiting for 6 months, returning to Canada for a months, then visiting the US for another x months. It is not likely, and is not sustainable. The general rule of thumb is to spend at least as long outside the US as in it, with twice as long preferred. CBP can and has denied entry if it looks like you are living in the US instead of just visiting.
My suggestion would be to visit for multiple shorter trips, returning home for at least an equal amount of time each time. Your partner can do the same - potentially swapping back and forth, as schedules can allow.
 
There are IRS considerations if you spend too long in the US.
There are potential health coverage issues if you spend too long outside Canada, and travel insurance might question residency if you spend too long in the US (normally travel insurance does not cover residents). Research the specifics beforehand.

hi
 
nope, that's one of the requirements to file as a stepparent, the marriage has to have taken place before the child's 18th birthday
 
so the USC will have to file for spouse and then the LPR parent file for the child
 
unless the parent came on a K1 and the child can immigrate on a k2 if it has been less than a year since the parent got the k1
 
 

But you said earlier that they approved the initial application, not your second one. You could've accomplished the same thing, much sooner and several hundred dollars cheaper frankly, by filing a petition for a hearing on naturalization -- 1447(b) suit -- pro se, or without a lawyer. USCIS magically finds cases when a judge is looking over their shoulder.

There is a section in the form where you have to explain your failure to register. You would presumably write that you were unaware of your obligation to register until after it was too late for you to actually register.
 
Yes, your statuses in that section would be your initial K-1 until your I-94 expired, then "out of status" until the day your I-485 was accepted ("received on" on your I-979C for your I-485), then "adjustment of status pending" or "I-485 pending" until your I-485 was approved, then "permanent resident" from the day your I-485 was actually approved.

Ok, so you were obligated to register with Selective Service the day you fell out of a lawful nonimmigrant status, which occurred on 19th July, 2014. And then once you turned 26 on 4th September, 2014 it was too late for you to register, since once you turn 26 you can no longer register with Selective Service. Unfortunately you were expected to register during those six weeks or so. And that kindof blows, but there it is.
 
So on the N-400 you would be required to answer Yes to the Selective Service question (that you were required to register but failed to do so). Now, if you send in your N-400 after turning 31 then you're not meant to need a status information letter from Selective Service... but honestly I would go ahead and get one anyway, because I know from personal experience it can take several weeks to receive it, and you'll be slightly screwed if USCIS ask for it and you don't have it on hand. 
 
To get a status letter you simply complete the following form and mail it in to Selective Service: https://www.sss.gov/Portals/0/PDFs/Status.pdf
 
As you say, if you apply once you turn 31 then your failure to register falls outside of the five year "good conduct" period and will not prevent your naturalisation.
 
There is an outside chance that you were automatically registered through your entry on a K-1. I don't think that happens; I believe only sending in an I-485 makes USCIS register you, but it never hurts to ask. So before requesting a status information letter I would call Selective Service tomorrow at 1-888-655-1825 and ask them to double check their records to see if you are registered or not. I assume you've already tried searching for yourself on their site and not found anything. Their phone agents have the ability to do a more thorough search of their systems than you or I mere mortals do.
 
If they verify that you aren't registered, then go ahead and send in the completed pdf to get a copy of your status letter, and file your N-400 once you have turned 31. It should no longer be an issue.
 
I also failed to register, and even though I am slightly older than 31 I still submitted a copy of my status letter with my application. At my interview she asked me to confirm that I didn't register, and I stated I hadn't. I pointed out that I had included a copy of my status letter, and then she saw it. And that was that.

Provided you have proof that you entered into the marriage in good faith then it's unlikely there would be any issue.

Yes.
And two i864s, two i765s and two I131s.

It seems that it is safer to wait a few days into the 90 day window......a few days won't really make a big difference in processing times.......

Because USCIS is a poorly run federal agency whose left hand often doesn't know what its right hand is doing.

You hire a lawyer to sue them for you, or you do it yourself. There are some DIY guides floating around on the Interwebs about how to do it.

two left hands, two right feet, assembled by the lowest bidder.

He should go the local Social Security Administration (SSA) office and apply for a social security card using Form SS-5: https://www.ssa.gov/forms/ss-5.pdf They accept walk-ins.
The section you are referring to is on the I-765, not the I-485. Since the I-485 was approved before the I-765 was adjudicated, USCIS did not forward his SSN request to SSA.

They are not issued by USCIS.  It may be requested on the form.   You might get it in the mail.
 
If you have an EAD go into a Social Security Administration Office.   Otherwise wait until he has the GC

No. 
 
They will hopefully have the foresight to do it themselves, but you cannot engineer it to happen. 

No. 
 
They will hopefully have the foresight to do it themselves, but you cannot engineer it to happen. 

No. 
 
They will hopefully have the foresight to do it themselves, but you cannot engineer it to happen. 

I would go through the office of one of your congressional representatives and try to get one of their immigration liaisons to help. 
 
It's beyond bullshit that their screw-up now becomes your problem through absolutely no fault of your own.