It can take many months for security checks to clear.

No not merely approval but using the AOS EAD.

You can apply at your local USPS for passport.

What is your question and where are you in the process for reinstatement?

Yes you can inform the officer at time of interview.

No a new signed and sealed copy is required.

You would indicate No as you already aged out by the time you acquired PR.

You may remain outside the US after case is approved.

Yes this definitely impacts your immigration status and possible changes to status.

Best to consult with an attorney to determine location of marriage and permanent resident prospects based on your personal history.