If your creatures are higher level than your healer than they may not like listening to your commands so don't try any nuzlocke challenges :P.
I like this part of the post, this will encourage players towards a competitive game and not toward a bang-and-loot styled mode.
The healers will level up 3x slower than a usual creatures, that's a bit tough, but I think you'll enable healers to restore a nice amount of health.
Will there be other support creatures such as healers?
Not in the support kind of way but there might be status effect moves, like lowering the enemies defense, avoidance, crit chance, etc.
The support units sort of adding extra HP, enhancing armor, boost stats.