Is Zombie Fortress Infection Pack free?

Yes. Zombie Fortress Infection Pack is released under Community and costs nothing. Neither it nor Team Fortress 2 has any paid content.

What do I need to run Zombie Fortress Infection Pack?

Team Fortress 2, which is itself free. Zombie Fortress Infection Pack is an add-on and will not run standalone.

The PlayBound Launcher installs it in one click from Team Fortress 2's mods list. You can also install it by hand — full steps are on this page.

Roughly 95 MB, on top of the base Team Fortress 2 installation.

Yes. The source is published at github.com/TF2-Zombie-Fortress/Zombie-Fortress under Community.

Zombie Fortress Infection Pack — Free Team Fortress 2 Mod · PlayBound