Yes, there have been a few times where I haven't gotten the classes I had planned on. This semester I am taking one of my back-up courses. Other semesters, I have been able to petition into classes I wasn't originally registered for. Often, the professor will save seats for people who absolutely need to take the course, or students can pick up the course during the first week of the semester if another student drops it.
There is only 1 triple room in each freshman dorm, so the chances of a first-year getting placed in a triple are extremely slim. As far as I know, the triples that do exist are also only on women's halls.
If you are placed in a triple, it won't be 3 people put into a room the size of a double. The room is larger (in fact, there are two separate rooms) and you also have your own bathroom for the 3 of you.