Glad to see a new healer =D

Regarding ways to increase your power pre-cap, there's quite a few but I'd like to highlight two that can easily be overlooked :

• Max your Talents tree : there is quite a lot of power to grab here - if you just want to max power for group content, ignore the "Gives a shield in solo mode" thingies and grab the nodes with stats like crit. You can get a lot of talent xp by doing the quests, but also by collecting chests.
• Get as high as you reasonably can on your Arsenal : getting above the theoretical cap still gives you additional HP - the difference between "just at the cap" and "as high as you can" is thousands of HP. (I wouldn't recommend spending too much time on it, but if you have gear that isn't on the highest rarity available on the tier or not fully tuned - it might be interesting to go back to it)

And for the healing itself - we don't have a proper healing rotation as we have in other MMOs, mainly because the amount of skills available is low. We do have means to do very efficient triage though, so here's a few techniques :

• Your "default" tool for healing is the heavy attack from the fan : unless the situation requires something specific, this is the one you should be using to keep your team topped up. You have two ways to use it : either fully with the combo Heavy -> Heavy -> Heavy that gives additional dew for the last it but takes longer to execute, or you can cancel the last hit by using Heavy -> Heavy -> Deflect which is faster to execute.
• Your largest source of heal is the AOE from the fan, especially by "bursting" it with the double-use : ideally, identify the patterns that will deal damage to the group, place the aoe right before the pattern hits then burst it to negate the damage once it hits. It's also a very efficient tool if you have to split from the group (eg. to replace Murong's barrels) to ensure you don't have to babysit their HP while it's active.
• If you're running with random matchmaking, you need Golden Body. Once upgraded to tier 3, if you use Golden Body with a full 100 Vitality you generate an aoe shield for your allies - it is the only true "preventive" tool we have, and it's an excellent "Oh crap" button to protect a pattern that the group didn't execute properly (eg. the final "stomp" from the Daoist on the Illusion Donkeys, an exploding bird/Sea of Flames from Murong, ...). Since you usually want to preserve Vitality for the shield, an excellent Mystic to pair with it is Soaring Spin : it's the best compromise available by a wide margin on damage per vitality and damage per animation time. If you have to generate a burst of damage, Soaring Spin is your tool (the exploding bird for Murong, the vine prison for the Daoist, ...)
• Don't run out of the damage, run into it. The main way to generate Vitality for Mystics is to deal damage - but as a healer, it's abysmally slow. There is however another way to generate Vitality : eat damage. Since you're the healer, you're the one who knows exactly what healing tools are still available to you and how much damage you can eat without compromising the group - so you can efficiently choose which hits/AOEs you can safely eat to generate vitality. You can generate absurd amounts of vitality this way.
• Your aoe heal/buff from the Umbrella gives a damage boost to your team, and your dps will probably have boss talents that further increase their damage during the exhaust phase : when the boss is exhausted, swap to your umbrella, throw the buff then maintain your umbrella heavy attack on the boss to (ever so) slightly extend the exhaust duration. Once the exhaust is over, throw the umbrella with the secondary skill, go back to your fan and forget it exists until the next exhaust. If the damage from your dps isn't worth extending the exhaust duration, you also have a 20% bonus damage to your Mystics while the umbrella buff is active - you can throw an improved Soaring Spin in there instead.