The colour of something is determined by how the electrons move around the atoms in the thing. If the electrons can oscillate (or vibrate) at the same frequency of the light, they interact with it.
In water they happen to allow all the colours of light to go through without interacting. But there is non-visible light that gets absorbed by water. If we saw in microwaves instead of visible light then water would appear black to us, and concrete would appear see through.
As for taste, I think most water has a bit of taste?
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