As for 1 and 2, I think given the choice, I would go probably make healing powerful, but gate that power more behind cooldowns. For healing to be impactful there has to be a failure state where you're just unable to push out enough healing for the encounter. Having your main healing spells on, say, 15-20 second cooldowns automatically makes any heals a precious resource. Not enough to be punishing for a single mistake, but enough for cumulative mistakes to cause deaths and wipes.
There should, imo, be a failure state where you're unable to hit the required HPS. For that to happen you need to be able to make mistakes with healing and right now unless you're outright ignoring your responsabilities it's extremely hard for a lack of healing to cause a wipe.
Gating it behind MP means you have failure states where you can't keep the HPS required up for long enough to beat the encounter before you run out of MP, but that's an issue which can be solved by consumables, gear Raid buffs and so on. It's a failure state that quickly disapears as more gear enters the equation.
I would also look to include more varied heals too, not just Fast/Slow and Expensive/Cheap etc, but things like the old Lightwell WoW Priests had, or being able to create healing zones and so on. Right now, things are very binary in FF14 outside of a few skills, rounding out the pool with more varied abilities allows a much larger range of healing niches to exist. Not just to shamelessly borrow from other games, but WoW's Chain Heal, Prayer of Mending and similar skills are much more interesting to work with than FF14's area heals.