Like QooER said, NEVER try to keep everyone topped off. No matter what healer, that is a waste of mp, because you will always overheal that way. Now, onto Sch things.
I believe this to be the most important thing, and the first thing you should do when entering battle, is place your fairy. She will stop healing if you move to try and follow you. Get used to placing her near the tank (make sure the tank is settled in). She will be far more effective once she is placed near them so she can turret heal.
Next, line up Rouse, Fey Illumination, and Whispering Dawn (you can switch the place of Rouse and Fey illumination, as long as both of them are popped before using Whispering dawn) because that is a buffer for you as it will regen the tank and everyone else. Once you pop Fey Illumination, you can just use Rouse+Whispering Dawn while it is on cooldown.
Third, as with any caster, always keep an eye on your MP. This is one part of all the "common" problems with Sch I don't understand. Aetherflow and Energy Drain is going to be your main method of keeping MP up. Now, I don't mean blow all your Aetherflow Stacks on Energy Drain, because you may need it for healing. What I mean is to use it during battle when Aetherflow is about to come off cd and you don't need to do any major healing. Spend whatever stacks you have on Energy Drain and then use Aetherflow. If you would like a good reminder of when it is off cd, you can use this macro for your Aetherflow button so that it makes a sound when it is off cd.
/macroicon "Aetherflow"
/ac "Aetherflow"
/wait 60
/echo Aetherflow available for use again! <se.7>
Activate Lucid Dreaming when at 50% and you shouldn't even need to do it for the rest of the encounter with the Aetherflow and Energy Drains.
Finally, onto healing. I will break this down into Single and AoE.
Single
When you have used all of Eos's abilities I said above and that isn't enough (it rarely is anymore), then you can use Physick. Only use Lustrate if you have the Aether to spare (it is coming off cd) or the tank is in immediate danger.
Don't try to keep up Adloquium anymore. It isn't worth it. Our shields are, apparently, not our thing anymore (must regain composure). The mana is far too much to try and keep it up since it mitigates so little damage. Now, don't get me wrong, you do want to toss one on the tank every once in awhile for that chance of a crit, but don't keep trying for a crit.
If the tank is not in the "Oh no, he is going to die unless I get a Lustrate off this instant" state and you know you have time to cast, do an Emergency Tactics Adloquium. This is our Cure II/Benefic II. You can only use this every 30s, but, it can do some good healing, and some great healing if it crits.
AoE
Like Adlo, don't try to keep up Succor for the same reasons you don't keep up Adlo, not enough efficiency to justify the cost. Succor is good, however, to toss out on occasion. It won't buffer much, but it is something. What your main focus is for AoE is Indomitability and Emergency Tactics+Succor.
That is basically it for the AoE. Keep up Rouse+Fey Illumination+Whispering Dawn, or just Rouse+Whispering Dawn. AoE is a scary thing for us Scholars. If Indom, ET+Succor, and a buffed Whispering Dawn can't do it, then clench your butt cheeks and pray for Thal to save you.
Other than that, here are just a few tips:
-Sacred Soil is rarely worth the Aetherflow. Example: My Lustrate heals for 11k. In order for Sacred Soil to have met that, it must have absorbed 110k dmg in that 15sec span. That's either only gonna be useful on huge pulls, or during the time where bosses do a large burst of damage (the phase where everyone is just standing there waiting for the damage is the best time for this.
-Speaking of Boss Bursts, this is the best time to use Deployment Tactics. As everyone gathers, use Adlo on someone and deploy it. It will be better than Succor overall (unless they all crit).
-Swiftcast+Emergency Tactics+Adlo/Succor is a great combo for when you know damage that can't be avoided is coming. You can hold them until after the damage goes off and instantly heal a good amount.
-Doing damage is a great form of mitigation. We only have so much Aetherflow and it is behind a cd, so ensuring mobs die before we are starving from lack of Aether and locked behind cds is key. Don't be afraid to toss out some damage. Even Shadowflare is a small form of mitigation since it has a Slow attached to it.