You cannot start your own tournament on an official way. However some groups do organize their own tournaments, it just takes way more organization and a cool volunteer that will keep track of the progress of the games played and the winners and losers and place the right persons against each other. So you can create your own tournament by starting a group and create a list of participants let them face each other and based on a realtime or turn based games give them deadlines before which they have to be ready so the second/third/etc/finale take place with people still having motivation.
For the games that were chosen to be picked for tournament play you'll have to wait for a moderator to answer as i do not know. Surely loads of questions have been asked about the subject and as said its been in BETA since forever. Which, i think is a direct effect from the mission statement of this site to bring a new game once every month. Due to not having enough staff and along with the long list of bug fixes that also need attention this is somewhat pushed to the long time planning.
Every1 can participate in tournaments. You just have to quick enough to enlist yourself as participant as all the tournaments only allow for 32 participants.
Enlistment can be done here: boardgamearena.com/#!tournamentlist
But yeah first come first served, meaning that tournaments for popular games are already full the moment they become available or you'd have to plan way ahead.
As such there is not really any condition as far as i know except that you need to sign in before its full.
Tournaments are real time. So you need to plan some hours for it. Due to real time there is a max time a game can take, however when you are very fast in your game you'll have to wait on the others to finish. So you can do something else or observe the game played by the other participants and check out the tactics of your next opponent (if you won!).
Cheers,
Sawyer
PS: sorry not in French, i just suck at the grammar

but if something is not clear i can try it!