No, you don't have notify immigration that your spouse died.

You can provide evidence of your assets if you wish.

I have never heard of either one of those forms. So it is impossible to advise you what to do except to see an attorney and show him or her what...

Yes, he can apply for an H4 visa without giving up his crewmans visa.

Perhaps you could put "change of status pending".

Divorce, by itself, is not a basis to deny naturalization.

If your spouse's ead and advance parole are based on your spouse's adjustment application, they should be approved.

You can and should file another application for extension of status.

File form I-765 and pay the fees to get the correct date of birth on your EAD.

There is no problem for you to get your H1b abroad unless you omitted information in your inquiry.