Not sure, but most animals that have vibrant colors that are used to distinguish gender or members of the species can see in color (think birds). I would say bettas definately see in color as they will attack colorful fish that they believe to be other bettas. Maybe not *all* fish see in color, of course, but I would suspect that most do. Hopefully someone who is not just theorizing can give you a concrete response.
Depends on the species.
The rule of thumb is that brightly coloured fish can see colour although their range is much wider than ours going right into the ultra violet at one end and infra red at the other.
Sometimes of course a creature is not coloured to attract its own species, but to warn preditors of it's toxins or foul taste.
As far as i know all fish can see in some degree of colour. Obviously some have better eyesight than others, and some species concentrate more on the infa-red spectrum of light, but I have not seen anything about fish only seeing in "Grayscale" (B&W)...
Plus, have you ever noticed the calming effect darker colors, especially greens seem to have? Ever since I read a post (somewhere on the net, can't remember now) I have used green backgrounds on my tanks. I hang green towels on the back of the tanks -- good soothing green colors and it is always handy to have a towel nearby. But, the darker colors do seem to have a nice calming effect on the fish -- safety in the darkness I suppose.