1. Is there a bandwidth transfer (and resulting Amazon charge) for files that exist in both the source and destination and are unchanged?
Yes. To compare files, s3sync fetches some information for the file on Amazon S3.
Example:
If you have a zillion files, s3sync needs to compare the zillion Amazon S3 files with the locally stored ones (to find out that nothing has changed. duh. but how else could it be sure.). There is little information flowing back to your machine, but each file is at least touched once. Resulting in a zillion times access. Amazon will bill you for that, and for the little traffic that was generated.
The total amount obviously depends on how often you care to check. If you are sure things change little, check less frequently. If you use S3 as a backup and have fewer files, it might not make much of a difference to to it more often.
