I think they’re called “hygienic showers” and it’s basically a small showerhead with a thumb button on the end to turn on/off. They’re getting pretty trendy with new construction flats.
The only downside is that they tend to drip a bit after you return them to the cradle.
It depends, but the place I’m staying at right now has it hooked up to hot and cold water with one of those sliding plate faucet handles.