No. Werewolf spawn during the Full Moon, and vampires during the New Moon. Each one of the four cycles lasts about 1.5 days real time, but you may see existing spawns outside of their normal moon phase if no one killed them.
No, but moon phases have nothing to do with it. It's just a popular urban legend (sorry Barkingllama ).
I have personally witnessed spawned vampires both under a full moon and under a new moon in-game.
Vamps and WW's spawn in reaper's march, bangkorai and the rift, at pre-determined locations (picked out of a pool of locations, not all of them are active at the same time) roughly every 3 real-time days, alternating between the two. The pattern is (again, roughly) day1:vampires, day2: nothing, day3: nothing, day4: werewolves, day6: nothing etc. etc.
The locations are shared between the two types. So when you see a vampire spawn somewhere, that is where you will find a werewolf later (its either exact same spot or very close, within sight distance)