I recently got a relatively cheap department store bike to bring to college, since it will see a lot of wear and will be kept in the elements. However, whenever I lift the front wheel (as in to get on a curb or start a wheelie), the fork tops out (by top out I mean, when I lift up, it reaches the most extended position, as opposed to bottoming out, reaching the most compressed position on an impact. This happens many times a day. Is this something I should be worried about eventually breaking the fork? Will it significantly limit the life of the bike?
I wouldn't worry about it. If a suspension fork bottoms out, it can hit the end of the compression with a substantial amount of force, but if it "tops" out the impact force is limited to whatever force the compressed air or spring can supply. This will most likely be pretty limited, unless you hear a loud thunk when the fork decompresses.
It's not impossible that it affects the lifetime of the bike, but it seems unlikely. But you should do regular maintenance on the fork just to be sure. If the construction that stops the stanchions from over-extending fails, the front wheel will fall off and that will most likely cause a crash.
Without knowing more about the construction of the fork it's hard to say for sure.
I would offer a guess that your fork slamming into its lowest position on your fork will not make it break any sooner than the fork would have if it didn't bottom out. Expecting a department store bike to be durable is unrealistic. A department store bike going through the kind of general care you describe shortens its lifespan even more.
It does make for an unsettling ride when it slams into position.
It might be best to avoid wheelies.
If it's annoying enough you could look into replacing the fork with one that is solid or one where the suspension works.