All of the technologies of night vision can see in visible and IR. By IR, I mean what's often called "near-IR", it's very close in wavelength to visible light, not the long wave IR that thermal vision systems use to view heat signatures. I don't know about UV, except that short wave UV would be blocked by the glass lenses of the night vision. I don't have access to a UV source that doesn't also put out some visible light.
Night vision amplifies the light, then projects that image on a phosphor screen. The phosphor is sensitive to a wider range of wavelength of light than our eyes are, so we can "see" IR and visible light with night vision. Thinking about how this is working, I'd be willing to bet the units have a range into the UV side that our eyes don't too, as well as IR.
The early gen 0 devices were so poor in gain and resolution that they were useless or pretty much useless without an IR source. They didn't see in low light any better than our eyes do, the only advantage was the wider spectrum they could see. For military use this can be a huge disadvantage, because all somebody needs is a gen 0 viewer, without the IR searchlight, to see you with your viewer/searchlight combination.
Gen 3 is so good that many viewers come with no IR illuminator at all. They turn an overcast no moon night into daylight. They let you see indoors, illuminated by that same light filtering through the windows. In a completely dark room, with no lights, of course they can't see, and they you need an illuminator. I built a small 1 LED illuminator for that purpose.
I haven't used Gen1 or Gen2, so the following is based on what I've read, speculation, and discussion with a friend who used Gen1 in Vietnam and has tried my Gen3 unit. With Gen1 you can see outdoors, but if your eyes are adjusted to the darkness there's not much advantage. The advantage is that gen1 night vision adjusts instantly and lets you see in "the dark", while your eyes take up to 30 minutes to adapt to very low light levels, and lose that ability quickly if exposed to bright light. Gen1 resolution is poor enough that on a moonless night, a slow moving camouflaged person can sneak pretty close to you without being seen. Some US troops that found Russian gen1 equipment in Desert Storm desribed it as "useless." (We're spoiled.) The reaction of my friend after trying my ITT 160 gen 3 was "holy cr&*". He had used the original starlight scope back in Vietnam.
I know less about the difference between gen 2 and 3. I believe gen 3 stuff is only available to civilians in the US, and is only made by ITT and Litton, but there could be others. I believe the main differences between 2 and 3 are the gen 3 tubes last a few times longer, and the resolution of 3 is higher.