You have 4 single target heals: Physick, Adloquium, Embrace (fairy) and Lustrate (Level 50). Don't use Cure. It has the same potency and mana cost as Physick but a Scholar using Cure is just weird.
Use those to keep the tank alive.
Adloquium gives you a shield to the same effect of the heal. If you get a crtitcal heal the shields effect ist doubled giving you a 300% shield. So on fights that require a lot of healing try to have an Adloquium on the tank most of the time and heal up in between those with Physicks. Adloquium is also great to have on the tank before he pulls enemies as it reduces healing on the pull and gives the tank time to establish emnity. Lustrate is an instant 25% heal using a stack of Aetherflow. Like an "Oh shit" button. The great thing about Lustrate is, it's a flat heal based on the target's HP ignoring any kind of healing debuff.
For party healing you have 2 tools. Succor and Sacred Soil (Level 45). Sacred Soil uses a stack of Aetherflow and creates a shield around an area. Succor heals everyone in range for a little bit and additionaly shields everyone for the damage healed.
Whenever your party isn't taking a lot of damage - you got a crit Adloquium on the tank or damage is low enough for your fairy to take care of the party or you are in an 8 man party and the White Mage can take care of the healing for a while - apply your dots. But make sure to do it in Cleric Stance. It switches your MND and INT and also gives you an additional boost on INT. Your attacks are a LOT more effective that way. Don't forget to switch out of Cleric Stance once you go back to healing.
I've been using the word shield a lot. So your job as a scholar has a lot to do with damage mitigation. Know when big attacks are coming and have the appropriate mitigation up.
As far as your fairy goes. Eos is a big help on healing. She has a strong AOE heal and also a cooldown that increases healing potency. Make sure to use Obey on Eos and trigger those 2 cooldowns yourself. Once you get comfortable with a fight switch over to Selene instead. She has cooldowns to increase spell speed and skill speed (which she alternates fine on her own so you don't have to use obey) that in the end increase the DPS of your party.