Employment change after getting green card - possible issues

There does not appear from this set of facts, to be any basis to revoke your permanent resident status.

Impact of filing I - 765 and I - 131 for AOS ( from H1B ) and then traveling outside the US soon after ?

At issue is whether a non-employment based adjustment is different than an employment based one, with regard to travelling on the H1b. You want to...

Married to US Citizen and living outside the US. No green card, but company willing to supply me with H-2 visa. Can this happen?

Immigrant intent disqualifies one for an H2b.

What is "likelihood"of U visa being granted with previous 20 year old drug conviction and illegal entry?

Yes, I have had U visas granted with drug convictions.

H-1 transfer. Does H-4 needs to be re applied ?

Yes, your H4 extension is not included in the application to extend H1.

My boyfriend became a citizen married to a citizen, divorced six months ago and now he wants to marry me and ask me?

If he is a US citizen he can file a visa petition for you and your minor child.

Changing nonimmigrant visa

No, he cannot change status to F2 if he is out of status. But he could leave the U.S. and get an F2 overseas.

There is a 10 year bar, with no waiver, for people who illegally reenter the U.S. when subject to a 3 or 10 year bar to admission - do to their...

What's the pension letter the immigration ask for from my I-864 co-signer and How to get it ?

The tax return and its attachments should suffice to prove her income.

Can I file H1 after my I - 94 is expired ?

As long as your extension is pending you are in status. If the extension is granted, you can change to H1b. You can file the change to H1b while...