It's normal for there to be scheduling changes.

Sounds like CIS will either deny or reschedule the interview. Wait to see what they send you.

USCIS accepts scanned signatures. Email it or send it to her husband and he can email or send it back to her. Do not sign for her husband. But...

A pending I-130 is not a basis for advance parole. In addition, no, getting advance parole will not have any impact on CIS processing your I-130.

I suggest showing it to a lawyer. If you are certain that CIS has not referred you for an investigation, you may want to file a mandamus petition....

If the move changes your required wages, then it may be an issue.

The U.S. government does not care whether or not he closes his business abroad.

If you are out of the U.S. more than you are in the U.S., you would not become eligible for naturalization.

You can file three years after you got the green card, whether or not you got it as a conditional resident.

It depends no doubt on the basis for your claim to be eligible to get paid in the U.S.