What happens to reputation if an upvoted answer is moved to another SE site?
The answer is deleted in the source site and the reputation is revoked. Votes are migrated to the target site with their respective posts, and if the answer's author has an account there, it will receive the associated reputation.
If a question which received some upvotes is moved to another SE site, what happens to the OP reputation?
Pretty much the same as above, except downvotes are cleared out, and that the question is left as a pathway for 30 days in the source site (reputation is only reversed after the question is deleted, i.e., after that 30 days).
Does her/his reputation on CV decreases, and the reputation on the other site increases?
Yes, if questions do have upvotes (there can be exceptions like a heavily downvoted question, which would make reputation increase in the source site after deletion, but let's keep it simple).
Or does the moved question start on the other site with 0 upvotes?
It starts in the target site with the amount of upvotes it had in the source site when migrated.
And what about comments? Are they moved together with the question or do they simply get lost?
Yes, all comments on any post are moved/migrated together with their respective posts.
References in Stack Exchange Meta: