Is it okay to exercise while I have a busted blood vessel in eye?

Yes. A subconjunctival hemorrhage is not serious. Avoid blood thinning agents like Aspirin and nsaids, but exercise in moderation is not harmful. You might want to avoid heavy lifting for one week to limit the risk of rebleeding.
Yes. If you are referring to a hemorrhage on the surface of the eye then it is completely benign unless there was associated trauma or it is recurrent. If so, an evaluation may be in order.