No, if your husband has not yet filed an I-485, he cannot file one based on an I-140 from a company no longer sponsoring him.

Check the receipt and go to USCIS' website to see if it is still pending.

It is not recommended to return to your home country at all until you are a US citizen.

It's probaby not an approval. When you get it, you can read it.

If you attended a school without complying with the SEVIS requirements, then you did not maintain lawful status.

File for change of status to F1 and enroll in a school that is not a public school and that issues I-20's.

Yes. However whatever you did that requires you to file the I-601 may have consequences that relate to your ability to travel outside the U.S.

There is no harm answering "yes" to that question.

A US passport is sufficient to prove you are a U.S. citizen.

No, the F2 is for a spouse or minor child of an F1.