Hm. No more common than any other type? There are people who specialize in them, but I haven't met any of those persons personally. And they do learn to cover their weaknesses! I had a friend who refused to use anything but water types, and he did well enough against electric-oriented opponents.

And yes! There are "egg groups", and if you pokemon aren't both in the same egg group, they can't breed. Your 'dex should give what group your pokemon are in if you point it at them.