Is Brood War HD Widescreen Launcher free?

Yes. Brood War HD Widescreen Launcher is released under MIT and costs nothing. Neither it nor StarCraft has any paid content.

What do I need to run Brood War HD Widescreen Launcher?

StarCraft, which is itself free. Brood War HD Widescreen Launcher is an add-on and will not run standalone.

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

Roughly 5 MB, on top of the base StarCraft installation.

Yes. The source is published at github.com/ShieldBattery/ShieldBattery under MIT.

Brood War HD Widescreen Launcher — Free StarCraft Mod · PlayBound