How does Time Machine deal with moved files
Time Machine works at the file level.  Change a single byte in a file, and it backs up again.  Move it into a new directory, technically it's a new file, so new backup.  There is no way to avoid this in the current implementation.  Ideally future enhancements to Time Machine will enable block level backups and some form of de-duplication, which will fix both the above scenarios, but for now you just have to be aware of it.  What you can choose to do, if you like, is confirm that the new location is successfully backed u p in the new place, and then manually remove the old location from your Time Machine.  This clearly doesn't prevent the need from repeating the backup, but it does at least stop you doubling the storage requirements.  Having said that, the old stuff will naturally get recycled off as it's no longer required should the backup drive fill.