What do I need to do to transfer my files to another mac, +more issues

Hey all, I'm quite new here but have learned a lot. I bought my first mac (imac 24" 2.66 GHz) during last summer and absolutely love it, but there's quite a few problems. To summarize:

-iSight camera doesn't work (never has)
-Mouse wheel doesn't scroll in the down direction anymore
-Keyboard's USB ports don't work
-Some minor software issue, for instance it'll say I can't eject a piece of hardward because it's in use, even if it's not, some freezing issues.

Good news is that it's still under apple care. I've been putting off addressing the above issues because I use the computer for work and haven't been able to afford losing it. Basically my questions are:

-Will they repair these things or just give me a new computer?
-Do I need to backup all my files and programs or will they do that for me (if changing computers).
-How do you transfer a program?

Are you using the mighty mouse? If you are, a cleaning will most likely fix that problem.
Do you still have applecare or is it still under the 1 year warranty? If it is, they will most likely fix it, as the issues aren't that major. I doubt you will change computers but I would do a back up myself just to be safe especially since it is a work computer. Are you talking about transferring a program from one computer to another? Which program?