Indeed, source is the game engine of Half-life 2. If you have bought the game you're free to make mods on the engine for NON commercial purposes just like with Half-life 1 (gold source engine). Making entirely new games is also possible, but you'd need a big budget!
on the free 3d game creators front....you've not got much out there.
Reality Factory, Jet3d , Desitny 3d, Antiyrad gx, 3d rpgbuilder 2004 & 2005......but that's about it for the freeware stuff....most anything else will cost you.Forgot....that hunk o crap called " Blender Game engine".