I agree with Jorriss. When people tell me they have the option of going to a university, but are considering doing their lower divs at a CC I tell them to think again! The coursework is pretty sucky at CC's (unless you get lucky) and applying to transfer is no fun (especially if you chronically overschedule yourself like I do). I got lucky and had a calc 2 instructor at my CC who proved everything, assigned proofs on the homework, and even put some on tests.
As for the getting used to the tests...
I do pretty average on the midterms, which have a lot of time pressure and very challenging problems (again, honors sequence courses). However, I scored very high on the final for which we had a decent amount more time per problem. I have improved my midterm scores every time by taking practice exams and working large numbers of problems under time constraints. I've also found it useful to memorize all of the theorems and definitions so they just roll off your tongue! But I tend to freeze up on these time-crunched, high pressure exams so you may not have the same problem (again, my only experiences are in honors courses so I cannot comment on the normal ones). As for the homework, I have only once not gotten a perfect score but that was also an A. The homework is comparatively difficult to the exams proportional to the time given. So like I said, if you're a good student and would consider yourself prepared... you will be fine, I think, but hard work and adaptation will probably be required.
As for taking the summer courses, I would recommend it! But I heard quarter system summer courses are only 4 weeks long... so it will feel exceptionally fast. Alternatively, if you can find an instructor who will let you audit in such a way that you can hand in homeworks and sit the exams I would highly recommend that! Then you could audit a hard course you will be taking the coming quarter, which would ease your troubles (or intensify your fears I suppose).