For the IAD issue, work on just dashing smoothly first before you start working on the IAD transition. I say this because, for me at least, I originally was very awkward when I'd switch from holding the stick to trying to dash, which often left me in a scramble to maintain control of the stick again (ie. I'd release how I'd normally hold the stick to basically palm-slap the stick in the direction I'm dashing). Another problem I realized was I'd stop, or forget to, hold down the stick to dash. For example, when I'd FRC Venom's Stinger Aim, I'd double-tap but then forget to hold the stick and Venom would glide for a moment and fall short of continuing the combo.
As for confusing punch with kick and all that, basically you need practice. That's all there is to it. You will soon adapt to your configuration and all will work out in the end -- until then, you'll just have to stick to training mode.
For how to hold the stick (sanwa-wise), I hold the ball between my index finger and thumb (index on the left, thumb on the right, sort of just on the lower end of the ball) and have my middle finger cross beneath onto, well, the stick. It just gives me a bit of control and helps not only for dashing forward but backwards as well. For transitions in, say, execution... either with Third Strike or GG, try performing super arts/over drives. Since both are normally fluid 236236 moves, or in some cases 632146, they'll get you used to trying out commands and executing more efficiently. Non-supers work as well, for example, one thing that helped me eventually perform Slayer's bite loop (when it was around in #R) more effectively was playing Third Strike for a while and messing around with Makoto and her command grab.
Can't help you much there, my stick configuration is...
P S D
K H R
I know it's not the "official" configuration or what have you, but it works for me. Always takes me a few minutes to get used to the feel of GG if I've been playing 3S though, and vice versa.
Hope some of this helped.
EDIT: I almost forgot, about your wrist... try to make sure you're in a comfortable position when you play, because you shouldn't be getting a sore wrist if you do that. Try to angle it perhaps, but generally just make sure you are in a comfortable position with the arcade stick.