Amateurs, except for the tennis players, the football players, and the bicycle riders. All of which are the big name stars who get paid to compete in other dedicated tournaments. I'm sure there are others too but those are the most promoted sports.
I don't think the ones above get paid for the Olympics though.
There are lots of professionals in other Olympic sports. Track and field, volleyball, swimmers, basketball, sailing, handball, etc. Usain Bolt is definitely a professional athlete (a sprinter) and so is Marina Alabau (a sailor) or Zhang Jike (a table tennis player).
Regarding compensation, it depends on the country, but I think many will get a bonus payment for medals or good performance. But anyway, the real money lies in advertising deals that athletes can get once they become big names (except for countries that have other types of compensation systems, e.g. North Korea).
Why so? The Olympic Games is the main event for professional track and field athletes, for instance, and if you're interested in professional sports - or any sports of absolutely leading edge competition, even when semi-amateur - then Olympics is the big event.
Oh many reasons. It is the most colossal waste of money. It is a horrible IP abuser. Almost everything surrounding it is massively corrupt. Some sports don't deserve to be in because they are not about (or less about) individual athletic performance.
Even if you like the competition those seem like strong reasons not to watch.
I personally think that if you are going to allow finely engineered shoes, poles, javelins, boats, balls, bicycles, then you should allow finely engineered bodies.
Amateurs, except for the tennis players, the football players, and the bicycle riders. All of which are the big name stars who get paid to compete in other dedicated tournaments. I'm sure there are others too but those are the most promoted sports.
I don't think the ones above get paid for the Olympics though.