I received Green Card as an RN on 6/23/2014. What portion does the employer need to pay for, in the process of E31 immigration?

I'd say that the only clear bill you would need to pay is for legal fees and filing fees for your adjustment of status. As a rule, the employer has...

Exiting and re-entering USA with a VALID F-1 visa, I-20,, and married to a US citizen. Problems re-entering? Or with AOS later ?

I'd say it is better to apply for adjustment of status and then travel with the use of advance parole.

Can I get any immigration benefits from the new bill after my TPS case got denied?

Maybe, IF the bill ever becomes a law; nobody knows.

I was convicted of a class 3 felony retail theft in 1992 and had satisfactory probation. no jail time. I was 26 years old.

You need to take certificate of disposition and minutes of guilty plea if there was one and show them to an Immigration attorney. If the...

30/60 days rule and IRS

Should not pose a problem; usually, things like marriage to the US citizen immediately after arrival does.

Have been waiting for 10 months gor deferred action and no respond only got a letter saying they are waiting for security checks

Just that: they are checking something... be patient; or hire an attorney to follow up for you.

I do not think it is a crime of moral turpitude; however, if I were, I would take a certificate of disposition and show it to an immigration attorney.

On G-325A last address outside the US of more than one year. I lived in Bali for almost 2 years but not consecutive. Yes /No?

If you stayed there for a year, put YES. I don't know what status you had there, but if you lived there, resided there, had a job, than it is...

Married to an usc who is involved in an illegal activity and threatening me of deportation. What should I do? Help me please.

You need to get help somewhere. Maybe domestic violence hotline. You can file for yourself but you will need to show that the marriage was real and...

Is it possible to change the status from B1/B2 to J2?what is the time needed

Should be possible; you need to file for change of status 45 days prior to expiration of the one you hold.