1°
Interesting proposition but have to be balanced wisely, with a group of priests maybe you can make a group of champions invicible for seconds. But at a certain point it can be useful even without being broken. Also, with this fast heal, you can consider that some can, in let's say 300 pop game, mass healers enough to constantly area heal army, because some priests would still heal while the cooldown has passed for others, so infinite heal. also, keep in mind that in fight infantry champions takes not that much place to fight so easy to heal.
Healing wisely would maybe counter massed ranged units.
2°I think medical center as you described it would be not that much used, pretty slow healing rate, if you don't have 5 healers in you better go back to nearest temple but i might be wrong.
Priests definitely need a change.