Yes the I751 receipt notice should suffice or a 551 stamp will work.

It is not advisable to do so without an individual having valid work authorization.

It depends on whether this was USCIS fault or not.

Yes you may travel domestically with valid passport.

The I94 information is needed but not the original document.

Yes you should apply for a new visa and enter this way.

Best to have an experienced attorney review your case history.

Best to consult with a state based family law attorney.

Wait for NVC to reach out to submit the DS160.

Yes this is still a possibility despite mistake.