The tournament will run for the same number of weeks as rounds a double elim tournament would run for the number of players who have entered. So a 16 man tourney would last about 5-6 weeks, maybe?
It's not a specific time every week, so if you have any tetris time in a specific week, you are likely to be able to make it, as long as you make that clear to whomever you're playing that round - you arrange the time each round with the opponent, making sure it's within the week limit. It can be played before the week even starts, of course.
And yep I'm very happy to receive any donations, even if you decide against joining. Of course if you do join, then you will be in with a chance of winning that t-shirt