No, there is no cooling off period. However the CBP officer does need to determine that she will keep to the terms of her visa if she is admitted.

There is no prohibition against marrying a U.S. citizen in fewer than 90 days after admission.

Being eligible for adjustment of status is sufficient explanation for why you are filing.

Yes, if you immigrate to the U.S. your social security payments will be credited to you.

H1b applications, including amendments, can take over six months. If you are planning to leave your employer, I suggest you skip the middle step...

I am not aware of any US law against that, so long as it is your real passport.

Yes. Bring your receipts with you just in case.

They should withdraw their applications. No, it should not be a problem when they return.

You must put your foreign address on the N-400. Even if it is inconsistent with USCIS records.

You could try contacting customer service and if that fails, the Ombudsman's Office to get it corrected.