Buy-movies from the iTunes Store would not expire.
Any downloaded file for buy-movies is valid for the device on which or through which it was downloaded. Not to be transferred to other devices. The external drive shouldn’t matter, but the playback device does.
Using the file with AirPlay or Home Sharing would require an online authorization, so that wouldn’t work 100% offline.
I don’t think the Apple TV app is expected to freeze when something is off for downloaded files. It should graciously prompt with an error message if it is unable to do some function.
Buy movies and TV shows from the Apple TV app - Apple Support
(Re)download TV shows and movies that you purchased - Apple Support
For macOS troubleshooting, try these:
Let us know the results of these tests.