Hi, my visit visa was already expired and I know that I need to apply within 1 year fro the asylum but I didn't apply till now. My 1 year will expire on first week of October 2015. I already apply TPS and my case is pending for the approval and EAD.
Once I got approved TPS and get EAD can I still apply asylum or not?
If I not apply asylum within one year " I mean within first week of October" then can i travel to my home country Nepal with AP and apply asylum once I come back to USA territory?

Note: AP helps me to exit and reentry so I can have a length to apply for the asylum whithin one year. Is it useful or not?
Highly appreciate with a suggestion.

The best option is to go out of US on AP, come back to US and apply for asylum.

@ MimroRamero
can I travel with AP and get reentry in USA territory or not if my case with TPS and ASYLUM goes parallel in immigration?

don't file asylum, the approval rate has been declined

If you apply for asylum then don't even think about going back to Nepal. You apply for political asylum and say you can't go back to Nepal because it is dangerous for you, then how can you go back to Nepal when asylum is pending.
If you have to go to Nepal then first go there, come back and apply for asylum.

don't do asylum you will regret. Just marry a woman.