If I delete files from iTunes, does Time Machine automatically delete them when I plug in my external hard drive? And if so, how do I change this?
No - when you delete a file on your mac Time Machine explicitly keeps all copies of that file that have been backed up previously.
The only caution is now you have all those copies on one drive (presumably) and it is one mistake / error away from being lost.
You can prevent this one copy deletion by periodically cloning your backup volume or otherwise archiving a copy of your machine separately than the normal Time Machine process to ensure you always have more than one backup copy of a file that you have now deleted on your main iTunes library.
Time Machine provides a backup of files currently on your system, plus an archive going back as far as drive space allows.
You can remove items from your iTunes library but not delete the files from your hard drive, in which case Time Machine will continue to treat them as "current" files.
If you're trying to remove the files to clear up space on your main hard disk, you'll want to transfer the files onto another external drive. A backup drive is not an external data store. You'll also want to be sure that the new external drive is somehow backed up. An external data store is not a backup.