Take Attorney Roger's advice and make sure to be calm and respectful.

What are my options (i.e. if I try to cancel the lease, will I have to pay moving costs? Can I compel her to pay to move it?)

Your liability will depend on the terms and conditions of your lease.

Is there any way to get out of the fee they are charging me or the lease itself?

How do you know they don't have any proof? Dogs must be walked, their mess must be cleaned up, etc.

You say you have already spoken to (at least) two attorneys - go back to them with your additional questions.

Just follow the instructions and they will explain what to do.

Am I going to be accused for fraud marriage ? I don't see how that's possible since he wasn't going to do me any papers

If there was no fraud, and you didn't try to get an immigration benefits, then you shouldn't get in trouble.

I have a pending asylum in Immigration court at San Francisco. Am I eligible for any medicad/medical or any heath benefit in CA?

You can contact the California Exchange for free.

This could be very serious - the fake id could be deemed as you claiming to be a U.S. citizen. You should contact an attorney directly.

Should I upgrade to Premium Processing? Should I wait for Decision or Leave before I94 Expiry? Can I renew MO Driving License?

I would just like to add that sometimes a PP upgrade can result in the issuance of an RFE - but this shouldn't be a problem if you have a good case.

Can I have dual citizenship at the moment of getting my green card at the American consulate?

You can have dual citizenship - good luck with your processes.