so now that I've already travel Nepal and got back, here's my experience. At TIA, I showed them my AP and passport and that was good enough. At Doha, Qatar, they had additional security screening before boarding on the plane to the USA, so the guy at the security asked my GC or visa and I showed him my AP and he asked for EAD, I showed him too and let me in. At port of entry in PHI, I showed my AP, EAD and passport and I was sent to secondary inspection after series of question. I figured I forgot to show my TPS approval letter and gave it to the guy in secondary inspection and everything went fine afterwards.