As long as you return to the U.S. before the advance parole expires you may travel anywhere your passport allows.

A civil restraining order should not affect you unless you violate it and get charged criminally.

Does the dismissal mean administratively closed or terminated?

Your Mom should file as the primary.

Yes, I would count them as he is supporting them.

If you are still overseas, communicate with the consulate to get this corrected.

Your home address is fine for the current work; for the previous employment you can list both independent contractor and the hospital where you...

As long as you continue to follow the requirements of the F-1 your student status will continue.

It should be fine. She will need to show her ties to her home country and intent to come only temporarily and then return for her immigrant visa...

That is perfect -- address where you will reside while in school.