You should find out whether you actually filed anything and perhaps get your own lawyer.

He does not need your help to stay in the U.S. and yes, you are obligated to support him.

Maybe you should apply for a visitor's visa, to visit the US to complete your probation.

Hard to say. Perhaps you could show a lawyer.

Here is the link to check https://www.uscis.gov/policy-manual/volume-8-part-b-chapter-4#S-C-4

You should be covered by the Child Status Protection Act.

It depends on the crime. If the crime is not one that subjects a person to removal, yes you can do it.

The I-485 processing times depend on your local office, not the service center.

Indeed it will. You would need to get the U visa issued abroad, and if the application is not approved, you would not be able to do that.

Getting a ticket is not an arrest. Often a traffic citation is not a crime. No rules have changed.