if I would do a run in 200CC, would it get classified with 250CC runs or as a different category?

Cups don't categorize by CC, but individual levels do.

If you run any of the cup runs you can do them in any CC you like, a few people ran 'All Cups' with 150CC.

Guilty as charged, however, I recently just did a run in 200cc, so I'll be submitting that soon.