You may apply for a visitor visa if you establish your eligibility. Green card prospects must be discussed with an attorney.

US naturalization interview, proof for travel records

Yes you may bring copies but the original passport may be requested.

It does not appear the waiver is required as he has remained outside the requisite 10 years. Consult with an attorney to determine how best to...

Green card for husband during grace period?

Yes you may begin the GC process while he is on the grace period.

Original copies should not he submitted. Consult with retained counsel for guidance.

I-130 and I-485 Concurrent Filling?

Yes best to file the I485 for her at this time given eligibility.

Do we need documentation that my husband’s ex-wife has agreed to give up custody and have the child immigrate to us in the US?

Yes you will need proof of permission from the custodial parent.

Can i travel to puerto rico with my asylum as pending?

You may with proof of pending asylum in case there are inspection checkpoints.

You should not enter the US with the intention to marry and adjust status thereafter. Consult with an attorney for guidance.

You may but it would contradict the intent required for a student visa.