You may use your spouse's last name, or not. It is up to you.

You do need to show you have been in lawful status since your last admission to the U.S. Ask your employer or attorney for the notices, or else...

You cannot change status if you are out of the country.

I do not believe CIS can approve the application. If you are a permanent resident, you can certainly file once you meet the eligibility requirements.

Provide your residency address outside of the U.S.

Reopen is not the correct word. You can request to recalendar your proceedings.

It seems to me that local would be better, but you could also provide state.

If you leave before the I-94 expires it's not a problem.

If you cannot afford to pay for the application, you are file an application to file without paying a fee.

Could be, if you did not respond on time to a request for evidence. Fine a lawyer, sometimes CIS is willing to give additional time for RFE...