I know siphoning strikes pulls stam and magicka per hit by trading off attack and spell damage. My question is does it also lower healing from a resto staff like it would for spell damage?
Yes, it does reduce the healing, but don't let that put you off, the skill is far too good to not have if you're healing. You will actually be more effective because you will be able to put down more heals.
With SS, do you toggle as required, or leave it on all the time?
I toggle as required--At the start of a fight (when your stamina and magicka should both be full), there's no sense in taking the damage hit. Same applies for fights that don't (or shouldn't) last long.
Not sure about the healing staff but Dawnbreaker morph is very useful for taking the edge off of the reduction in damage, although I run Leaching Strikes instead.