Is Subway Station Battle Arena free?

Yes. Subway Station Battle Arena is released under CC-BY-SA-4.0 and costs nothing. Neither it nor SuperTuxKart has any paid content.

What do I need to run Subway Station Battle Arena?

SuperTuxKart, which is itself free. Subway Station Battle Arena is an add-on and will not run standalone.

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

Roughly 16 MB, on top of the base SuperTuxKart installation.

Yes. The source is published at github.com/supertuxkart/stk-addons under CC-BY-SA-4.0.

Subway Station Battle Arena — Free SuperTuxKart Mod · PlayBound