Skimming back through the book, I was wrong about Logain, my apologies on that one. I think I got myself confused with Logain's interaction with Mat, where it is the kind of interaction I'd expect from Mat, but at the same time quite blunt and undiplomatic, so when in my mind I assigned it to Egwene, it didn't seem Amrylin Seat kind of behaviour.

Regarding the leaders, it just felt to me that she was willing to make deals with them for short term gains, such as trying to get them onside against Rand, but with no real view on the long term impacts of these, which as Amrylin Seat I feel she should have, as her concern should have also focussed beyond the Last Battle.

Then also personally insulting the Dragon Reborn in front of other leaders wouldn't give them a lot of faith in what she may also decide to say about them in a diplomatic setting, which is hardly a way to build respect.

Her only concern post the Last Battle seemed to be on determining to take Tuon down, which seems foolish to me, unless she is planning on taking the entire Empire down (which would provoke a large conflict within the Empire, which would possibly spill over borders), it seemed personally against Tuon, which is even more foolish given the whole damane thing would continue after Tuon left, and was there long before. Also, bringing up the fact that Sul'dam could channel in front of Tuon's court is a good way to try and destabilise a rule and empire, which is hardly the thing to do when the Last Battle is about to commence.
Regarding Tuon being an insane sociopath, she didn't come across like that to me, just as someone who had to be seen to wield power strongly by her people, as her hold on power is tenuous, as Rand saw and said to Tuon (though notably not in front of her court, just her personal guard who are likely to be well aware of the situation). I think Cadsuane may have liked to spank Tuon, but would be wise enough not to go down that road with her, knowing that the Light needed the Seanchean on side, and how Tuon was key to that. After all, Tuon at least had a tie to Mat, the next ruler is even less likely to go with Rand's agreement.