How did the jaguar, a cat known for crushing the skulls of its prey, not bite Lara's wooden bow in half?
Most likely because it's made from strong wood. Maybe black iron wood.
Also, while a skull is stronger than many things... it is a hollow shell with soft tissue inside. The haft of Lara's bow is solid wood, which is probably harder to outright crush.
Why the hell did Trinity land their High Council in a unsecured location in the middle of a running battle against an unknown number of enemies while suffering heavy casualties? It really makes no sense for them to risk their lives, and it doesn't hide a lazy attempt to conveniently wipe the entire Trinity organisation then leave fans wondering what happened to the rest of them in future games.
Possibly arrogance? They had tons of heavily-armed soldiers defending them, so they probably felt that a bunch of primitives such as the Yaaxil couldn't do anything to hurt them.
Dead in Tombs
Who or what killed the Trinity mercenaries in the Tomb in Cozumel Lara begins the game in?
Who or what killed all the Yaaxil in Thirsty Gods tomb at the Mission of San Juan? Trinity? Something else?
San Juan Mission
How the hell did Trinity know to pop up at the Emperor's tomb? Two Serpent Guards go in with the correct password, then suddenly Rourke is blithely roaming the streets of an Incan relict city in his modern military gear without anyone being the least concerned about it, and gunning down the queen. But it gets weirder - Trinity could not possibly know what clue Lara found in the tomb, so why on Earth are Dominguez and Rourke cheerfully waiting on the surface to snatch Jonah after Collapsing Floor Trap #902 separated him from Lara?