It appears your waiver was denied. Consult with an attorney for guidance.

The petitioning spouse should request expedited processing.

No you must file a separate petition for your father.

The priority date on receipt should indicate this.

One sister should act as substitute sponsor for humanitarian reinstatement.

Yes you may travel internationally while your case is pending.

It may take up to 120 days post interview for decision.

The LA marriage doc should be sufficient for proof.

It depends on USCIS processing times for I130.

Depends on your state RMV, likely not however.