It depends on the spell/ability.
A living conjuration CAN be healed. But, the spell you use to do so must be able to target it.
Heal, for example says "living creature" in its target line. So it cannot actually be cast on a mana flower, despite it being living because its not a creature.
The ability/spell target options must include "Conjuration", or simply "Object" in order to be able to target the conjuration.
Sleep is the same deal.. its target specifies "living creature". I think conjurations all have psychic immunity anyway though, which would also prevent sleep.