*This is in no way meant to be anything other than the way I, personally, choose to heal in the Scholar role. I do not theorycraft, so I don't know if it is the most efficient, but I do know that no ones ever dies or complains about my healing.
First, and most importantly: MACROS
Currently, macros are what separate the noobs from the experienced. I'm sure that will change, but get off that noob train! Here are macros that you should always have stocked:
/micon "Energy Drain" <-- This is the #showtooltip equivalent for FF14
/ac "Energy Drain" <t> <-- These two lines will let the spell cast no matter who you have targetted.
/ac "Energy Drain" <tt>
same macro for Physick, Bio II, Miasma, Bio, Virus, Succor, and Leeches
Second: What separates us from WHM?
1. Battle ressurection. (getting the lvl 26 THAUM spell swiftcast or whatever it's called is very important to make this spell insta cast)
Battle Ressurection is important in all aspects of party play. Tank dies to spike damage? Swiftcast > Ressurection, boom! He's back in the fray. I even use this spell on the 8 second timer and it is still worthy.
2. Miasma and Bio/Ruin II to some degree
Miasma and damage dealing. It seems a lot of the community overlook this aspect of our class. Miasma prevents 50% healing on the mob. There have been several fights in my early career where this has come in handy (the dragon fight and the ant queen fight). We should be casting Bio II and Miasma whenever there is a lull. With the proper use of Energy Drain and Aetherflow, you should never be low on mana, so get those dots in!
[FYI: I usually wait until about 60% MP, then Eneregy Drain twice and Aetherflow and am back to full MP.]
[Pro Tip from Mobbaren: Keep Ruin II in the rotation as well because most bosses aren't immune to Blind]
3. damage shields
Don't spam Succor unless your tank is getting demolished. Precast Succor II when you know the team will take guaranteed damage. I.E. After titan jumps or when that worm in CC does the dust storm.
4. our pets.
General consensus is that the AI is stupid and needs fixing. I agree, however, I do think that even being stupid, the pet does take a massive amount of stress off of our healing.
Do we have a healing rotation?
Being that we only have two single target spells, probably not. Succor if the target isn't already shielded, Physick if it is already shielded.
I also think that upon hitting 50, I will make an Eye for an Eye / Lustrate "o $h.t" button. I hope that this was helpful, any suggestions please feel free to add.