Yes, but it won't be a visa stamp. It will just be a copy of the same stamp on the I-94.
She just gets an I-94. For re-entry, she needs a copy of your I-797, a copy of the marriage certificate and a copy of your I-94.
She needs to file an I-539 extending her H-4 status. It should be filed...
If the original H-1B was not cap exempt and you have not been outside the US for a year, you can claim cap exemption on your new H1B. I'd also ask the employer to start the GC process if your plans are to remain in the US long-term.
This could be interesting. If CBP processed the I-94 they will consider her out of the US, which means that the I-485 will be denied - they will assume she is no longer physically present, or she entered without inspection.
Almost certainly. They have a record of your entrance, and they other have a record of your exit (in which case they know you overstayed), or they don't. But since you are interviewing outside the US, the consular officer can request proof of your departure date from the US.
Please tell me you...
USCIS could not unless they had the SS-5 where the alien made a false claim to US citizenship under penalty of perjury. They can't revoke citizenship because some clerk mistyped things into a computer.
You need to stop worrying.