He had no reason to be up there on his 2nd death. He doesn't have vision on the bush, no allies anywhere nearby he sees Chovy who he can't possibly beat in a 1v1 at that point. If you look at the map, SKT even pings the brush. So they were more than aware of the possibility of Tarzan being there. Faker walking up there was greedy.

TP play is an obvious ???

Going in on the E onto an Alistar, with no vision on Baron side and a Kalista ensuring his safety meant he put himself in a compromising situation that at most gets a Kalista ulti. After having wasted his TP, Faker has no way to re-enter the Baron dance if he backs so he's stuck half hp after having gotten nothing. He could have survived the Baron fight if everything else had been the same and he had hp, saving them the game.