If you look at early Tyrannosaurs like Guanlong, Proceratosaurus, and Sinotyrannus (maybe), they all have these funky crests on their head, but when you look at later species, there is no visible crest, so why did they lose these traits?
No actual direction to why they lost the crests, they just eventually lost them in favor of other things, though some may argue the crests are still present even in Tyrannosaurus albeit just reduced.
As far as I know, the large prominent crests were mainly traits of the proceratosaurids, which most likely didn't evolve into the later tyrannosaurids.
That is an interesting question. Maybe its bc its arms soon became display like carno. and wasn't there like a preserved dewlap on a tarbo. this could mean they had air sacks