I am currently on OPT/F1 extension which is expiring in July. I have TPS with EAD.
My Question:
1) Do I have to maintain a valid status( such as F1 ) even though I am in TPS?
If No, will I have any problem changing my status to F1 (after my current F1 lapses) at the end of the expiration of TPS?
2) Can I travel back home with a Advance Parole after my OPT expires but before the TPS ends?

No, you do NOT have to maintain a valid F1 status, if you decide to use TPS.
However, your SEVIS will be released, and your F1 status will be terminated.
After the TPS expires, you have 60 days grace period to either reinstate back to F1 status, or return to Nepal.

Reinstatement might be tricky, because you have to prove that you were out of status because of severe economic hardship, or mistake by your DSO. As long as you can create strong documents to support your claim, you should be able to get reinstated to F1 visa. However, if your reinstatement gets rejected, you have to return to Nepal.

That make sense. Thanks for the reply!

Anyone going through the same situation?

If I were you I would not give uo the F1 status.