No, making a bank deposit will not impact how or when USCIS processes your i-130 application.

USCIS officers understand that most marriage based applicants today have no social security number and no way to get proof of joint assets.

There is no harm bringing all of your documents to prove you maintained status.

Seems to make more sense to change them to H4's.

Yes, you can apply for a new work permit based on the pending i-485 without paying any filing fee.

No, a parole stamp shows a person was paroled into the U.S. It is not a document that allows one to travel out of the U.S. and be paroled again.

The various state Departments of Motor Vehicles each have their own rules. USCIS does not determine who is allowed to drive.

Until CIS tells you why you are not eligible to adjust, you need to wait for their decision. if it takes over six months, file a petition for writ...

You could file an i-589. You may be eligible for some other benefits and so you should meet with an attorney to discuss your options.

You can make any argument you want. If you convince the adjudicator, you win.