back up on external hard drive, deleting movies on computer?

Backing up and deleting is not backing up. Backing up is always having two copies of everything, preferably on completely separate drives in different locations.

In order to play something through iTunes it has to be added to iTunes. You can add files from a separate drive to iTunes and have them remain on the drive by holding down the option key while adding but you may find it irksome to continuously see broken links if the drive is not attached while using iTunes.

You can apparently stream movies from iCloud to an AppleTV, but I can't provide details. This should work for you unless it is one of those items no longer in the Apple Store (and your reason for always making sure you have a copy on your drives).

Apple TV can stream your movies and TV shows (from Apple's servers) if they are purchased items from iTunes Store. They are shown under Movies -> Purchased and TV Shows -> Purchased. Other videos that you added to your iTunes library (on the computer) manually can be played on Apple TV over your home (local) network, but those need to be stored in your computer's storage.

What I have been discussing is having part of your media on the internal drive, some on an external, but having your library files on the internal drive. A "library" is a whole set of files working together, just like a city library is more than a pile of books on an empty lot somewhere.

More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management

What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html

What you see in iTunes is not your actual files, it is a text listing of what files iTunes remembers you having added to iTunes minus the deletions, and pointers to the actual files it should try to play upon request. So if you keep a movie file on an external drive and that drive is not attached when using that library iTunes will pop up a ! saying it cannot find the file it is supposed to play. This doesn't really matter for the most part since unless you actually want to play that movie having a broken link it won't make a difference if you are playing music on the computer. Some people find it annoying though, and I guess it could be misleading because you could have broken links that do matter but you won't notice them if you have a bunch that don't.

I don't have an AppleTV (ATV) so I don't know the details other than what I read about them. I do not think it is possible to get an AppleTV to read your files directly from a hard drive. A movie stored anywhere except in iCloud has to be read by iTunes and sent to the ATV. Alternatively you can do as I mentioned earlier, and Kenichi Watanabe described in more detail, and that is stream the files directly from your iCloud account to your AppleTV.