Nerve endings receive pain. The brain "feels it".

So it can easily be made to feel pain -- just pass in the same signals the nerves would have.

"floating", "silence", and "black" are sensory states. There's no assurance that a brain in a pool would feel any of these. It's hard to know what a brain will project as it attempts to construct a reality matching that for which it evolved.

But it's reasonable to use these terms since they're the best approximations/guesses we have.

Also, people who become blind later in life often describe it as "black", so I think it's reasonable to assume that's how the brain would interpret lack of sense.

Your brain can't hurt, but presumably a phantom body could be made to hurt by providing the right neural stimulation.