Well if you have a day job -- even though as in your case it's ski instructor -- and also compete in some races then you're not a professional. You have to do nothing but compete to be considered a pro. Think of it as the professional athlete's job is competing, and when he's not competing he's training.

Now clearly there's grey area here. For example if you compete for a living but also happen to have a part time job for a couple afternoons a week to help make ends meet I would consider you a professional athlete. Likewise if you have a full time job during the off season but are still able to find time to train so that you're ready when the season starts again.

Olympic athletes can't be earning a living from their sport, ie. are not professionals. Only in this sense are they amateurs. The term as used here has nothing to do with skill, and clearly so because to compete at an Olympic level you have to be the best of the best. It only means they aren't competing for prize money or have a sponsor (yet).

A pro can become an amateur (presumably to go to the Olympics). And vice versa.

Hockey is an exception where they do use pros on the olympic teams. There may be more sports that allow pros, I don't know.