She can apply for a visitor visa on her own.

Best to have an attorney review the notice to appear. Good luck.

You may but will likely need proof of the same.

You can apply for extension but reentry right after departure will likely not be allowed.

Yes this likely indicates the approval of EAD.

It should have arrived by now given timing. Contact USCIS for guidance.

Yes that is normal and U visas don’t show up.

Yes you may do so after 5 years of being a LPR. Consult with an attorney to discuss your sons cases.

Best to apply for naturalization certificate first.

Yes you may do so on a valid issued visitor visa.