My question is related to unpaid internships in New York city, for Human Services/Social Work positions when out-of-status

The agency still might require you to have a valid work authorization. There is always a chance that ICE will try to deport you if you are out of...

Will i be able to work and be in legal status after PERM I140 gets approved and waiting for I485 Green card to approve?

You need to speak with the company's lawyer about the details of these arrangments.

H1B Petition Approved then revoked by USCIS . Am I cap exempt

I do not think you are cap exempt.

Removal of the 2 years conditional status

You will need to amend your petition and present proof for the waiver grounds.

Can I withdraw my application from my agency; request for a release letter and look for other agencies?

I think that you have to talk to an Immigration lawyer ASAP to see how you can save your started green card process.

L-1 to H-1 Ammendment

You need to speak with the lawyer who is handling your H1B petition.

How long time does it take to check background during naturalization process?

There is no set time. Unfortunately, sometimes it takes years.

How to ask to stop working when a case is not yet opened

You simply ask your lawyer to stop working on the case. The amount owed will be determined by your agreement with the lawyer.

L1B is an employer-specific visa. You need to consult with an attorney to go over details and if you will be able to accomplish your plans without...

Does the 60 day waiting period since entering the US refer to the non-immigrant's entry with the current status or the last one?

I think you should consult with an Immigration lawyer before you do anything.