Forum Moderators: open
It seems that the application queue is a bit clogged up at the moment, and there have even been bugs in the procedure. The times I remember hearing about go up to two months. If you're in doubt, then you can ask the metas in their public forum.
Do you get a rejection letter
Not necessarily. It can depend on both the processing meta and the details of the application. But in general, at least a form letter is sent.
Btw: One important thing to make sure is that you got the first confirmation e-mail immediately after you applied, and replied to that. This "double opt-in" system makes sure that nobody is signed up against their own will. If you didn't get this confirmation request, then you either mistyped your e-mail address, or there was some other glitch that caused the process to fail.