WOW, great topic!
Okay as far as reproduction goes, those are PURE vampire demons. Any human they infect would be tainted. (Example would be to look at Anya's speech about pure demons during Graduation Day... I believe pt 1). I have a weird feeling that it's possible for a Turok-Han to infect a regular vampire though, and in that case, they'd be a bit more pureblood. I may only have that perspective because I've seen Blade II and there was a breed of vamp which fed off and infected both humans a normal vamps. If you guys haven't seen the Blade series, I'd recommend it. Really bad ass.
2. It's quite possible that after the Scythe "Slew the last demon who walked the earth" that the Turok-Han were in hiding down below. OR it's also possible that the Hellmouth isn't considered to be "walking the earth" but only being in this dimension. On that note, I have a further query about how they THRIVED down there! My only explanation for that is possibly that the Turok-Han were able to sustain one another with their own blood, OR that they also feed on demon blood (assuming there were other demons camped out in the Hellmouth, or who emerged from *insert hell dimension here* and into the Hellmouth as a means of attempting the enter our dimension)
3. Are there any left? Yeah, probably. That was an EPIC number camped out in one location, I'll grant you that, but there must be other locations and/or Hellmouths which would house such creatures. I know that on the show there is a Hellmouth in Cleveland, but just because only two were mentioned, that doesn't mean there aren't others. Quite honestly, I would expect there to be one in Africa or the Middle East at the very least. That area (Egypt, Mesopotamia, Sumeria) is the cradle of life, so it stands to reason that the earliest doorways into our world would crop up there. There might also be one somewhere in Asia I would say as well, because civilization thrived there as well after the first migrations of humans.