Yes your sister can complete the COA through I865.

Depends on the particular court’s schedule.

Best to discuss with your retained counsel.

Yes this applies to unlawful entries to the US.

No this shouldn’t be considered public assistance.

No this is not possible after legal separation.

Yes you may do so with an expired passport.

The invitation letter should likely not he required and will have limited value.

It depends on current processing with USCIS.

No this would not be considered as petitioner.