When a question is migrated, is the reputation earned by its author on the original site subtracted from the author's total? What about votes? Badges? Do the same rules apply to the question's answers?
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Answers / Reputation
The answers on the migrated questions are deleted from the source site. This means, as with any deleted answer, the reputation will be removed.
Question and answer votes are preserved on the destination site and are cast by the Community user. These migrated votes will confer reputation.
If the user on the origin site does not have an account on the destination site, the reputation is held for that user until they do create an account on the destination site (so long as they use login credentials which are connected to their other Stack Exchange account).
The votes will earn you badges on the target site. Badges are never removed from any user, however it does mean you will not earn the "next" badge of that type.
(some of this may change a bit over time but that's how it is now)