1 nest to control all vales on UFH manifold?
The Nest can only control one zone at a time, but that's ok, because it sounds like there's only one "control zone" in your system.  

Your heating system may work better if its split into three sections, but since the will all come on at the same time, the Nest should be able to control all three at the same time.  What the Nest can do is control each zone separately.  

Typical control systems have a "hot" wire and a "common" wire.  Just tie all the commons together and all the hots together and then run a single common and hot to the Nest for control.