1. I thought it was fairly out of character for them to behave that way, not to mention it just seemed far too comical and farcical for them to be carrying on a quiet conversation on the side while Rand is supposedly negotiating with Tuon/Fortuona. Their conversation itself was still entertaining and funny though, so as with so much else in the book, I found myself enjoying, and disliking it at the same time.

2. Perrin and Slayer were both using their willpower, it's just that they were both such masters of TAR that they couldn't battle each other on the simple stuff, and their struggle shifted to the tiny details that lesser dreamwalkers would never even have thought of. I actually loved those scenes, because it advanced what we had always known should be possible in TAR, and showed for once what someone unconstrained by silly traditions and superstitions could accomplish.

3. Maybe, I don't know. It's not important, and isn't any worse than Egwene and Vora's wand that in the last two books became the equivalent of callandor.

4. I was disappointed by the ease with which Rand defeated the DO in the end, but I remain of the opinion that he misunderstood the scope of the battle. Like with the Pattern, which he could only comprehend by perceiving it as an actual Pattern, his mind had to find a way to comprehend the DO. So what he thought was the DO wasn't the entire being, which is beyond human comprehension and not even a being at all. And we did learn something about the DO's nature. I'm convinced now that the DO is the antithesis of choice, so he would have been perfectly happy with Rand "killing" him. That would have been the real victory. And likely the DO can simply bide its time and wait for turning after turning until Rand does make that choice, or gives up. When you have infinity on your side, you don't have to try very hard at any particular occasion.