Hi @Elkayj. In order to play your videos and/or music on your Apple TV, you will need to turn On Home Sharing in iTunes. This will allow you to access your iTunes library on Apple TV, turn on Home Sharing in iTunes on your computer using your iTumes Apple ID.
As for moving your iTunes library to an external drive, you will no to go to iTunes Preferences and select Advanced. There you will see ITunes Media folder location. Click the Change button and select the external drive and directory where you wish to keep your media files. I would suggest you also check "Keep iTunes Media folder organized" and "Copy files to iTunes folder when adding to library".
For more detailed instructions, the following two links may be very helpful to you:
- iTunes for Mac: Moving your iTunes Media folder: http://support.apple.com/kb/HT1449
- How to move your music to a new computer: http://support.apple.com/kb/HT4527
I hope that helps. Good luck!