Yes, you can file such a motion so long as the case is pending.

Generally it is safe to travel in and out of the U.S. if one has advance parole.

I am not aware of any law that requires U.S. citizens inside or outside of the U.S. to notify any particular agency of their address.

It depends on the purpose of your trip to the U.S.

The sister can petition for him, and so can the mother as long as he is single, or even if he marries if she naturalizes.

It's actually common sense. The CBP office must decide based on how it looks whether they are living in the U.S. or just visiting the U.S.

You could contact OPLA and ask if they would agree to administrative closure. You have a right to request a continuance to await the I-130 approval.

All question will relate to whether she will keep to the terms of the visa. In addition, you may be detained and put in removal if you try to pick...

No. Terminal 5 at O'Hare will process them and they will be admitted as asylees.

There are provisions to get a religious exemption for taking vaccines.