No, marriage to a US citizen does not automatically disqualify one from a J1 visa.

When can I get married and file for green card for my spouse ?

You may file at any time however the previous marriage and sponsorship will likely impact a subsequent case.

Can a judge reject a political asylum case based on sex orientation at master hearing?

More information is needed about your claim. Consult with an attorney for further guidance.

Marriage Annulment while Being a Derivative of an asylum case

Yes your sister may apply on her own at this time.

You will have to wait to be rescheduled as this is not done based on request.

You may apply now given valid visa status for your spouse until 2023 and visa bulletin for F2A category being current. Best to consult with an...

I-539?

No you do not need to apply for I539 with pending AOS.

No your visa should not be in jeopardy if your parents use that as temporary residence while I539 is pending.

Changing address married to USC?

Yes it may be delayed if you relocate, but uncertain how much of a delay.

No this should not impact future reentry.