Can I use a tap and die set to change screw threads? I'm having difficulty finding the right size of screws for my project, and wish to manufacture my own. Can any type of screws / bolts be used with a tap and die kit in this manner, or do they have to be made of a specific material?
If you're trying to completely change the treading on a nut or bolt with a tap and die, I don't think that's going to work very well. You may be able to get a new thread pitch, but it will be interleaved with the existing one, and all you'd be doing is weakening the thread material.
If you need to simply fix some mangled threads, then have at.
If you're looking to cut your own bolt threads, you will probably want to start with unthreaded rod. Although, as Cathode mentioned in the comments, if you have hardened steel rods, you're in for a lot of frustration and not much success.
I suppose you could chuck the bolt into a lathe and carefully (very carefully) slice the existing threads off to give you an unthreaded rod with with a nice bolt head, but then you'd have to grab a box of nuts of sufficiently small size that once you ground the threads out of the inside the resulting diameter would match up with your newly "skinified" bolt stock & you could rethread those.
All in all, I'd head to the local big-box and grab a box of what you need for your current project. You'll have some spares for the next project, and will, eventually have a few dozen of everything lying around that you can't find.