If you hit Tab while in the game, you'll see a section for analog controls. Sounds like decreasing the analog sensitivity might help. I'd do this on a per game basis rather than global, since you don't want to hose up the regular games.
Can only venture a wild guess at your second question, but I suffered similar symptoms from a stuck button. The system would sometimes run normal, then go crazy and run real slow. Initially, I thought it was a computer problem.