No, there isn't anything to secure the chair other then it's brakes. When you turn the chair it pretty much wedges it in. Other then the 3 bumps and they tell you when you will feel it right before it happens it is very smooth.
Yes, as you can see in this picture the sides were low enough for her to see out.
I did Characters in Flight about a year ago. They ended up needing me to transfer to their wheelchair because mine was a little wide for the entrance to the balloon or something. My personaly wheelchair is has an 18x18" seat, but due to some weird axel stuff the chair is about 27 1/2" wide. It worked okay for me because my personal chair has bad brakes and theirs has good brakes. That said, even with their wheelchair (which I would not recommend for Pooh sized folks because it fit me well and I'm not particularly large) I couldn't turn to the outside. That ended up working fine when I went because my neck is fused so I can't turn it around as much as I can and we ended up being up there as the fireworks were going in both MK and EPCOT so because I was faced in a more "neutral" direction I could turn to see both, whereas if I'd been pointed just outside on where I was in the ring of the basket, I wouldn't have been able to turn enough. I'm 5'4" standing and probably about 3' 6" seated and could see over the edge without too much problem. To get off, I had to go all the way around the circle because there wasn't room to turn around or anything. I actually really loved doing it and would go again.
The one major warning I'd have is that, along with obviously not being good if you have problems with heights, it can also get a bit rough. When I went we ended up being the last flight of the night because while we were up the winds hit 23mph and they have to stop running the balloon once the wind hits 20mph. While it's a very solid balloon, 23mph at the top of their tether does create a fair bit of motion. One of the friends I was with had suggested going up because she's been trying to conquer a fear of heights and she was ultimately okay with it, but there was definitely some non-child friendly language coming out of her on the way up. Once we hit the top she was better. It probably didn't help her on the way up that we were a bunch of geeks and another friend was asking a bunch of technical questions. That said, the answers he was getting made me feel even more safe.
You can see a picture of me on Characters in Flight at http://www.lczajkowski.com/2011/11/04/uds-p-day-4/ at the bottom of the post. (Not my photo so I don't want to upload directly here) The friend who wrote that post is the one with the fear of heights so the paragraph above the photo is a description of her experience.