Yes! All three are correct. I think the first and the third option would sound most natural when speaking.

All of them are grammatical and they all have the same meaning. English allows speakers to drop the "to" in an infinitive if it is understood. The conjunctions "or" & "and" can be followed by the verb without the "to" thereby shortening the sentence but not losing the meaning. She wants to exercise and (to) run. She wants to exercise and (she wants to) run.