Could be that a supervisor needs to review it and it is no longer ready to be scheduled for an oath ceremony.

Possibly. If you can find yourself placed in removal proceedings you may be eligible for cancellation of removal.

The question is poorly written. It seems to me the 'three years" is referring both to departure and to 180 days unlawful presence. As applied to...

Your employer can file an I-485J. The fact that you are working for the government, by itself, is not generally a basis for an expedite.

No doubt the consular officer will consider the marriage. That alone it seems to me would not be enough to base a denial.

It depends on the asylum officer and the judge. If your fear is not based on your race, religion, nationality, social group, or political opinion,...

You should assume that there is a significant risk that USCIS will reject the application if it is not dated.

Your employer could file a PERM and later an I-140 for you. You might be eligible to file for adjustment of status. But you will not be permitted...

They will maintain your records permanently.

You should not need to submit it at all, unless you got your green card other than based on your marriage to a U.S. citizen.