Actually for perception of depth, there is more to it than needing two eyes. You need two eyes for stereopsis. However, the visual pathways of the brain use other clues, as well as stereopsis, to judge depth such as pictorial cues (relative height, shading, linear perspective etc.), and motion cues.
1. No, healthy eyes both 'see' the same colors. Both right and left eyes have the same specialized organs called 'cones' that enable color vision.
2. Yes. You need two eyes for good depth perception. Here's a good explanation:
http://www.vision3d.com/stereo.html