Water molecules ARE actually very slightly blue colored, which is why the ocean appears blue, but the amount in your pool or bathtub isn't usually enough for it to show without a coloring agent.
Okee dokee the molecules ARE NOT blue, the materials dissolved in the water can be slightly green-blue, however, most of that blue color we see comes from the shadows formed by the depth of the water, and the remainder comes from the refracted light bouncing off, being absorbed, or being 'bent' by the water. Green/blue/indigo/violet are shorter wavelengths, so they respond differently to the water's electromagnetic wave refraction and absorption properties.
Not necessarily. While that can be a factor for the very surface in bright daylight, the ocean itself is actually blue due to shadows and refraction, as I mentioned before. The reflection of the sky accounts only for surface color. Actually, I have read a few things supporting the idea that the sky is more in reflection of the ocean.... but I'm not completely sure how legitimate those ideas are.
"Shinji was a bitch-ass hoe who deserved to die!"