You can absolutely be a character performer while on the CP, however there are very strict criteria relating to height and build. If you want to be a character look-alike then you have to look a LOT like the character. They will line you up with heaps of other people and choose the best one.
You are not required to take classes but you can if you want. Some of the classes I've heard of are 'personal branding' and hospitality related stuff. If you decide to take classes you will get 2 days off per week, and will be required to take a 4 hour class at Disney University on each of those days. There are exams, presentations, etc just like normal university.
As for Disney careers, there are some opportunities. If you have an engineering background and do lots of networking it's possible to get involved in Walt Disney Imagineering (degree required), however it's not easy to get your foot in the door. A lot of CPs end up moving down to Florida and working here full time because they like the lifestyle. Some end up as coordinators and managers, but unfortunately most just end up working as full time cast members.
To be honest I wouldn't give up your dream of being a teacher to work for Disney. Like I said, opportunities for progression do exist, but are very hard to come by. The college program is a lot of fun and you'll meet a lot of great people. But in the end the reality is that if you move down here with the hope of gaining a career you'll more than likely be disappointed.
Good luck!