Yes you may do so without any fee.

You may sign the form for your minor child.

It is not advisable for you to travel to your home country that you claimed asylum from.

Contact the asylum office to request case be expedited.

You should apply for the J1 waiver through marriage to USC.

Depends on your mothers status. Consult with an attorney for guidance.

Best to have an attorney review his criminal history before travel.

Best to work with an immigration attorney to review your case.

Your marriage must be for good faith reasons.

Yes based on current address although you can request change.