How is sambo organized in Russia? is there a pro-league?
do you go several matches in one comp?
Is it like MMA that any styles are allowed to partake?
There are FIAS organized/sponsored tournaments. They are the largest ones. You could say it's the "pro" league (even though it's an "amateur" sport). But there are a lot of other organizations or promotions or gyms that organize sambo events. That's why you sometimes see different uniforms and/or rules allowed at one competition or another. There's some combat sambo organizations that wear no helmets and allow knees to a grounded opponent, for example, while FIAS doesn't allow that.
There is supposed to be an elaborate ranking system of points according to your competition record in FIAS, and the category you fit in according to your ranking.
However, most competitions are open to everyone even if you're not ranked (because de facto, there's no real record of points/ranking in usage), and even if you are not a sambo practitioner (as long as you wear the proper uniform and follow the rules. In FIAS tournaments you do have to register as to what federation/association you belong to, but in many countries there's none, so you just sign up as your gym. If you are from Zimbabwe and sign up as "Zimbabwe MMA", i don't think they'll care.
In theory, to enter a World/Continental/Regional/City championship, you have to be the champion of your country/city/gym. In reality, if you are from X country and go and register at the World Championship, and there's no one else from your country in that category, you will get signed up. Unless someone well known disputes the fact that you are no champion, they won't stop you.
You do go several matches in one competition, depending on the number of participants, just like in BJJ. This can be particularly grueling in combat sambo tournaments. I've seen tournaments where you need SEVEN wins (in the course of two days, maybe one (the number of matches is supposed to be limited per day, don't remember the exact number now)) to be the champion.
So sometimes there are a lof of byes. A good example is when Fyodor Emelianenko gets to win some of his matches by his opponent not fighting at all. A lot of people will criticize them... But if you just fought HARD 3 times, you are injuried and exhausted, and you have to fight Mr. Emelianenko who just KTFO and ippon'd his opponents in under 1 minute...