Is KOTOR III: The Jedi Masters (Part 1 of 2) free?

Yes. KOTOR III: The Jedi Masters (Part 1 of 2) is released under Free fan mod (see the download page) and costs nothing. Neither it nor STAR WARS™ Knights of the Old Republic™ II: The Sith Lords™ has any paid content.

What do I need to run KOTOR III: The Jedi Masters (Part 1 of 2)?

STAR WARS™ Knights of the Old Republic™ II: The Sith Lords™, which is itself free. KOTOR III: The Jedi Masters (Part 1 of 2) is an add-on and will not run standalone.

How do I install KOTOR III: The Jedi Masters (Part 1 of 2)?

The PlayBound Launcher installs it in one click from STAR WARS™ Knights of the Old Republic™ II: The Sith Lords™'s mods list. You can also install it by hand — full steps are on this page.