Yes, it works great on Chrome.
Regarding the missing collisions: ThreeJS focuses on the 3D part of a game engine only. If you want collisions, you need to add a physic engine.
There's a couple of them out there - I would recommend CannonJS and there is a working ThreeJS FPS with WASD and collisions here: https://web3dblog.wordpress.com/2013/01/07/source-code-of-th...