You may relocate and file a motion to change venue upon doing so.

You may but she abandoned her application upon departure.

Yes you may contact USCIS to inform them of your concerns.

Yes for a VAWA application, it is important to submit ample medical evidence.

Indicate date to as present date for this purpose.

Yes you need petitioner photos and beneficiary photos. Refer to form instructions for specifics.

Refer to USCIS processing page for guidance.

It depends on whether you have filed I765.

Yes it should be ok if received by date of expiration.

Yes you will need to establish parent-child relationship through BCs or secondary evidence.