Is Hotkey Casting free?

Yes. Hotkey Casting is released under Community / Open Source and costs nothing. Neither it nor The Elder Scrolls II: Daggerfall has any paid content.

What do I need to run Hotkey Casting?

The Elder Scrolls II: Daggerfall, which is itself free. Hotkey Casting is an add-on and will not run standalone.

How do I install Hotkey Casting?

The PlayBound Launcher installs it in one click from The Elder Scrolls II: Daggerfall's mods list. You can also install it by hand — full steps are on this page.