Do I need to get invited to a tournament? I'm asking because I would like to play a tournament with my mates, but isn't it only the 'pros' WHO can play in tournaments?
For most tournaments you won't need an Invitation. I've personally played 3 tournaments where i just had to register my team and then we could start Playing.
But i'm Not sure if that counts for every tournament. If you want to play LCS you will have to be a pro player in a pro Team. If you just want to play an online tournament you can write an application and hope that you or your team will be accepted.
Only because it's a small online tournament that doesn't mean there's nothing to win. In fact you can even win a triumphant ryze skin in an online tournament as long as riot is supporting the tournament (and they do that quite often).
Of course you won't win the big 100'000$ in a simple online tournament but I've seen some where you can actually win 1000$ or even more.
But you also have to keep in mind that even in these small tournaments there are Diamond 1 Players which are Hard to play against if you're Not At least Plat 3 +.
But hey just try it. On www.lolking.com you can find tournaments every week with prizes like gaming gear, riot points or even Cash.