How to file for political asylum?

An asylum application does not call for submission of original documents. You need to read instructions to the form I 589 carefully.

Does USCIS send the I-797 Approval Notice for AOS (I-485) EAD?

You should be able to use your card as a valid proof of employment eligibility. You should show the notices you received to your attorney.

Got approved on the spot with a signed paper but 4 months later got rfe,.Are my evidence that submitted enough?really scared

It is unusual to receive an RFE afte an interview if it was not discussed with an officer. You should consult with an Immigration attorney.

What's the expiration of my H4 EAD

You will need to file for a new EAD.

You should contact your employer's Immigration attorney immediately.

My h4 extension and ead extension file currently still pending . my

I believe one in H4 status can work only with a valid authorization unless a category for EAD you filed allows for an automatic extension.

Can i travel to Puerto rico while my asylum case is still pending?

PR is a US territory. You should be OK to travel there as long as you can show that you have a pending asylum case.

I539 denied on basis of more than 30 days in the USA after I94 expired and Program start

That's a common mistake, F1 status seekers are making: they do not check when the program starts and waste their time, money and hopes on doomed...

Voluntary Departure? Why Not Termination?

I doubt you would qualify for VD at this point. If you are looking for a second opinion on how to proceed, you should really meet or consult with...

If I have a B1/B2 Visa stamped for the US. Can I visit the US for leisure trips too?

I am not sure what was the purpose of your application, but usually, yes, you can use your valid B visa for tourism.