Sounds like you are a U.S. citizen and sponsored your husband for his green card? He should have conditional green card and he will need to remove...

If you are on F-1, you cannot work without work permit.

If you are on valid H-1B, you can travel while your I-485 is pending at USCIS (since it is dual intent visa). But please be advised that leaving...

If his only purpose of coming to the U.S. is to marry you then I think you should do K-1.

That would be against the intent of B-2 visa.

You can initially file for H-1B Change of Employer for part-time and you can later amend it to full time when it becomes full time.

Assuming you are a U.S. citizen, you can file her I-485 now if she is in the U.S.

I would suggest you call the lawyer to check if the filing fee checks have been cashed out.

As long as it arrives at USCIS before your H-1B expires, it should be fine. You might want to ask the lawyer or your employer to file it overnight...

Providing designs would be considered as work.