When a random event occurs, the bot client takes over and works its magic. During that time, are any of the methods(onLoop, onPaint, onMessage, etc) in a script active?

No. Based on my experience.

Well, just talking out of my experience, there's one of two possibilities. There are two main scripts I've been running with OSBot so far. one, if I leave alone, I find myself stuck in a random area, or have failed a random event... With the other, I've never encountered the problem... So either the scripts do have influene on the random event's outcome, or I've just experienced more luck with the latter script.