Is Heart of Gold Campaign free?

Yes. Heart of Gold Campaign is released under Freeware / Community and costs nothing. Neither it nor Dungeon Keeper Gold has any paid content.

What do I need to run Heart of Gold Campaign?

Dungeon Keeper Gold, which is itself free. Heart of Gold Campaign is an add-on and will not run standalone.

The PlayBound Launcher installs it in one click from Dungeon Keeper Gold's mods list. You can also install it by hand — full steps are on this page.

Roughly 24 MB, on top of the base Dungeon Keeper Gold installation.

Yes. The source is published at github.com/dkfans/keeperfx under Freeware / Community.

Heart of Gold Campaign — Free keeperfx Mod · PlayBound