If you reserved a room only,then you can cancel up to five days before your check-in date. If you booked a package, it must be cancelled or paid in full by 45 days before check-in. If you pay it, then cancel within that 45 day timeframe, you pay a cancellation penalty. Hopefully others can say what it is - I've never done a package.
Once your cancellation is processed, you usually have your money within a week or so. Disney says it could take two billing cycles.. I cancelled a room only reservation recently and had my money that same week.