Even if so, the I751 should be okay and approved if otherwise eligible.

Best to contact NVC to inquire directly.

Yes you should sign the travel document but best advised not to travel to country of refugee.

Best to check the requirements on USCIS webpage for I864P.

You may do so by filing form I130 for your sibling. Process takes 12-16 years until visa becomes available.

No unfortunately the PCC is required.

Yes you may file for AOS as soon as you become a USC.

You can’t after the applicant has received their PR through you.

It may have been sent in error and can be disregarded.

Continue to wait but be patient. This processing time is completely normal.