Since you have an EAD, apparently you can work. Whether you can get a job depends on availability.

I was sent an i20 as being accepted for phd admission from top one unversity. inand going for an f1 interview next week.

Do consult with an experienced Immigration Attorney for guidance.

First H1B petition older than 6 years but physical stay of only 5 months

No. Not "cap exempt."

Is it safe to say after I turn the RFE the next step is decision

Great question. One that is impossible to answer.

Old warrant of arrest from immigration court for failing to appear since 1995

If you had a Notice to Appear, you may have been removed in absentia. Do consult with an immigration attorney for assistance.

Questions on getting married to a US citizen and staying here during the petition process.

Do consult with an experienced Immigration Attorney to discuss your options.

Can green card permanent resident holder can get married and give the paper to the husband?

I agree with Attorney Segal. Do consult with an experienced Immigration Attorney for guidance.

MY CHILD'S FATHER SIGNED FOR THE FIRST PASSPORT BUT REFUSES TO SIGN THE SECOND RENEWAL. WHAT DO I NEED TO DO IN ORDER TO FILE

I agree with my colleagues.

Probably not. But you could benefit from a consultation with an experienced Immigration Attorney.

Tell the truth at passport control?

Do consult with an experienced Immigration Attorney for guidance.