#1 - Tyrande's always been emotional and way too attached to two things: Elune and Malfurion, ever since Warcraft 3 she's been like that... and I actually like it better than the weird pacifist, almost passive ways she and the nelves had during most of WoW.
#2 - I agree to an extent. You gotta put it into context - Jaina'd been holding a grudge against the Horde, and all of a sudden Dalaran switches and allows the people who killed her family and Theramore to be back there. It would've been bad if she put her hatred aside... she's endured quite a lot of bad shit. The other route would've been becoming an enemy of the Horde and the Alliance.
#3 - She wasn't angered, she was cornered because she underestimated the strength of the Night Elves and she thought that Malfurion's fall alone would break their spirit. The burning of Teldrassil was her winging the situation... and it worked, at least judging by the cries and the run make up of Delaryn on that short.
I think the problem here is that people still see women as emotional wrecks but fail to see that emotions have also been part of most men's narratives in Warcraft, as well. Arthas got his unholy pants on a twist because a woman was stalling his conquest of Silvermoon so he tortured her and turned her into his personal ghostly slave, for example... but no one says he's an emotion-fueled children lashing out.