I am not 100% sure but I have heard that you can travel to USA with an expired TRV and a valid permit but only through land border. Any other type of crossing - water, flight etc, you will need a valid TRV.
Again, I have no way to confirm this but I have had friends who have told me so. However, if you are unsure, don't take a chance and apply for a TRV.
Of course you need a valid visa to enter US.. which I believe you do.
Let me share my experience, even though I did not even think about my visa which was expired already one year before when I went US. So with out getting this point in my mind. I went US with valid work permit but from land border. Everything was Ok I went there and come back nothing was happened with me ALHAMDULILAH.
Possibly but if you go via plane or something else it is different situation.