I need an advice from immigration attorney

It is case by case.

She can not recapture the time she spent as a H4. The PERM application must be pending over 365 days.

If I apply for residence for my mother who is living in Mexico, can she come to the US while she waits?

No. She has to wait in Mexico.

Can A "conditional permanent resident" green card holder petition for me?

She can.

If DOMA is knocked down can my partner of the same sex petition a green card for me? He's a US Citizen.

I agree with my colleague. It is unlikely.

You have to discuss the matter with your current attorney or hire a new attorney and have him/her reassess your case.

Understanding processing time

I agree with my colleagues.

Immigrant spouse recently good faith marriage end in divorce. Married again to USA citizen,. Can my new spouse file i130 ?

You have to file a I-751 divorce waiver first. Your new spouse can not file the new I-130 until USCIS make a decision on the I-751.

Visa Stamping of H1B and H4.

Your previous B1/2 entry should not be a concern.

I mailed my papers 6 days ago the checks for the i-130 and i-485 were cashed but the check for i-765 was not cashed why?

The filing fee for I-485 includes I-765 and I-131.