Your entire application must be reviewed by a licensed immigration counsel.

No, there is no other lawful way for you to petition a sibling to care for your child unless you submit an au pair J-1.

No. Your LPR status will not be compromised once one submitted a timely I-751.

There is no expedited way for a biometrics appointment and if one appears at the center without the correct date for the appointment the personnel...

Once the live criminal warrant is entered it requires one's physical presence to quash and recall it, unless a retained counsel somehow could...

Your family member most likely is inadmissible and will be barred from adjusting entering the U.S. unlawfully.

Engage a local immigration counsel to determine whether your criminal case generated a warrant for your arrest and start from there.

How long are you planning to remain abroad even after you son submits your N-400?

You may consult further with a counsel of your choice without any delay.

Your current I-94 controls your lawful duration of status.