Is Battlefield 40K - BF1942 free?

Yes. Battlefield 40K - BF1942 is released under Free fan mod (see the ModDB page for terms) and costs nothing. Neither it nor Battlefield 1942 Anthology has any paid content.

What do I need to run Battlefield 40K - BF1942?

Battlefield 1942 Anthology, which is itself free. Battlefield 40K - BF1942 is an add-on and will not run standalone.

How do I install Battlefield 40K - BF1942?

The PlayBound Launcher installs it in one click from Battlefield 1942 Anthology's mods list. You can also install it by hand — full steps are on this page.