Hmmm, let's see:
There is a variety of bell pepper that matures from ivory to orange to red. It is called Romanian rainbow and I will be growing it this year. But most "green" bell peppers will mature to red if left on the plant (for example, most will be about 70 days to green but 90 days to red). If you want a mature yellow or orange pepper, then the variety will have to say that. Usually seed catalogs picture the pepper when mature, but all will start out green. (So Yes, different plants for different colors).
As far as crossing peppers, yes they are horribly promiscuous. But if a hot pepper crosses with a mild pepper in season 1, the fruit off the mild plant will be mild, but if seed is saved and planted the next season, the fruit will be hot! Any pepper crossed with hot will be hot (in most cases anyway--of course there are degrees of hotness). But I've never heard of people breeding hybrids of peppers for fun, guess that's more of a tomato thing. But it's certainly doable. I'd just caution about eating the peppers before you know just how hot it might be!