I think Nynave has always been a bit of a bully with the temper to match. Where was it that she thinks about the time she was 16 and got into a fight with another girl. Didn't Ny throw a bucket of water on her and the girl came back swinging?

If Ny hadn't been made Wisdom so young, she would have had to temper herself. But since she was Wisdom, people showed has respect and accepted behavior from her that they wouldn't have had she still been an apprentice.

But she's grown and matured as the books go on.

As far as people hating Egwene, I've always liked her. The woman in these books can be annoying she's by far from the worst in my opinion. That scene with her and Ny, I've always found it hilarious. Here's Nynaeve completely thrown off balance from her former apprentice, and gains a new found respect for Egwene as a woman. Only for us to find out that Egwene is still a child in many ways and was simply trying to not get caught doing something she wasn't supposed to be doing. Hysterical!

I don't think it's all that big a suprise that Mat could beat Galad. Didn't Thom at one point tell him that he has the fastest hands he's ever seen? (Sorry, can't remember which book)

Mat is a natural when it comes to the quarterstaff and ashanderai just like he is with his knives. It all has to do with the quickness of his hands. His skill with the ashanderai is a natural extension of his skill with the staff. I don't think it has anything to do with his new memories and everything to do with his own skill.