I got my asylum approved as lesbian. Can I now marry a guy who is on H1B visa ? My green card is in process.

Your initial asylum claim will be highly scrutinized given the marriage. Consult with an attorney for further guidance.

If you are currently a F-1 student and If you get TPS, is it possible to transfer to another college without new student visa?

Yes you may transfer to another school without another F1 visa.

Immigration law?

No this likely was in error as your case was approved.

No you should wait for the actual appointment notice.

Yes a lawyer can assist with explanation of this incident.

What should I answer (Y/n) “For the purpose of complying to USCIS, have you ever been arrested or charged for breaking any law?

Based on the information provided, the answer would be yes, even if the record was expunged.

As you are working in Nevada, best to list this address.

What is the amount of money a petitioner should have in his account when submitting correspond. paper to NVC if he has cosignor?

I would recommend using a cosignor as $10,000 will not be sufficient for support purposes.

Citizenship

You may apply as many times as you wish and immediately after denial. However best to work with an attorney to do so.

Can I leave after the limit day that I placed on my i539?

Yes you may depart and can notify USCIS that you are withdrawing your application.