Is KMRP: KOTOR Modern Restoration Patch free?

Yes. KMRP: KOTOR Modern Restoration Patch is released under GPL-3.0 and costs nothing. Neither it nor STAR WARS™: Knights of the Old Republic has any paid content.

What do I need to run KMRP: KOTOR Modern Restoration Patch?

STAR WARS™: Knights of the Old Republic, which is itself free. KMRP: KOTOR Modern Restoration Patch is an add-on and will not run standalone.

How do I install KMRP: KOTOR Modern Restoration Patch?

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