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).