Is Boeing 777 Series (777-200ER / 777-300ER) free?

Yes. Boeing 777 Series (777-200ER / 777-300ER) is released under GPL-2.0-or-later and costs nothing. Neither it nor FlightGear has any paid content.

What do I need to run Boeing 777 Series (777-200ER / 777-300ER)?

FlightGear, which is itself free. Boeing 777 Series (777-200ER / 777-300ER) is an add-on and will not run standalone.

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

Roughly 180 MB, on top of the base FlightGear installation.

Yes. The source is published at github.com/FlightGear-Community/777 under GPL-2.0-or-later.

Boeing 777 Series (777-200ER / 777-300ER) — Free FlightGear Mod · PlayBound