US Immigration from Peru

I sent my application last week. USPS says it was delivered to USCIS Chicago P.O. Box, but they still have not cashed my check. It has been almost 1 week. Any ideas on the time frame?

Been seeing mixed messages about whether getting married on a K1 before applying for a SSN is a bad idea or not.

Situation -

Fianc and I will fly from Peru on Nov 1 to my parents house. My father is a minister and wants to marry us there that before we travel to my city. Talked to county clerk already and got application and a form to fill out if your partner doesn't have a SSN. Seemed pretty straight forward.

Will I have problems with the SSN office, trying to apply after marriage? Would like to get her SSN as soon as I can.

Should I apply with her maiden name? Not sure if this could cause problems with AOS.

We recently file our case, September 25th to be exact, and I m wondering whats the best way to follow it and be able to know what agency will be processing it, NOA S, etc.

Also, will the agency handling our case be related to the State where it was filed, like if we did in Arizona, will it go to Texas or Nebraska, maybe?

I am a US citizen and I got arrested for theft and got convicted of disorderly conduct 20 years ago. Will this be a problem with my 129f? I disclosed everything on the form.

The parents of my spouse are planning to come visit us in the US on tourist visas. My spouse is currently in the AOS process (biometrics are done, just waiting for advanced parole and a green card interview date). My spouse did an AOS from a tourist visa. Is there a risk that her parents might be turned away at the boarder? If there is a risk, is it high, and are there any ways to mitigate the risk?