It very well may depend on the reason CIS provided for denying the extension of status. But assuming they are still in H4 status, and their...

He can apply. He may have a hard time convincing the consular officer that he has no intent to immigrate to the U.S.

There is no requirement to live with your husband as long as you can prove that the marriage is entered in good faith.

if you know you have been approved, you are required to begin working with the new employer.

Unless someone else controls your wages and hours, you are self employed. Use the same address you use on your business income tax returns.

You could call and ask them, or you could wait for a decision.

If you are allowed to work and get paid, the employer can pay you more than required, and can pay you a bonus without violating your status.

If the consular officer did not mark on the B1/B2 visa that it is cancelled, then it is not cancelled.

Form i-131 is an application for advance parole, refugee travel document, etc. Perhaps you mean a different form?

No. If he did not request it in the application, nor at the interview, his only way to do it is by going to court.