Can I use Apple TV without internet
Can I use the internet from my iPhone to airplay a movie onto my home tv through the Apple TV?
Question marked as
Yes you can, as far as Apple TV is concerned. Connect it to your personal hotspot and play.
Would this be a home video stored on the phone, or a movie from a streaming provider?
Not all streaming providers allow AirPlay (notably Netflix).
It is a different issue if your mobile provider ******** such use. Not all do, and if the do, it is up to a data limit.