Your case is adjudicated on its merits.

This is not an immigration issue. Go to family court to address problem.

Yes, you can file II-130 petition as H1-B holder.

Yes, you may travel abroad while your AOS is pending.

While USCIS is processing your TPS, you can remain in the US.

All jobs should be listed on I-20. Contact DSO with concerns.

Bring to the attention of court you are not a USC.

In general, Canadians do not need a visa to enter the US. Some are admitted as B-2 for a certain duration. If you were admitted as a B-2, and...

You should provide more background to your question. It appears you started from the middle or somewhere else, not from the beginning.

It is possible. However, the question should be what your chances are to succeed. The burden of proof is so high that few to none are able to...