Few tips for a mistweaver monk.
1. Keep Renewing mist on 6 targets all the time.
Around 10 seconds before aoe damage spike, use Thunder Focus Tea, Uplift and start gathering chi.
At the moment of damage spike you will have 9+ targeted covered by Renewing Mist and 4 chi. Use 2 uplifts. If you have Chi Brew talent and need more healing - you can use 2 more Uplifts.
If there is no aoe damage in nearest 1 minute, use Thunder Focus Tea on cooldown.
2. If you are out of mana and you can afford to spend some time, that's how to recover it: go Tiger Stance, use Jab to gather full chi. Go back to Serpent Stance, use Blackout Kick or Tiger Palm to utilize your Muscular Memory buff, discharge the rest of chi with whatever (Uplift/Blackout Kick), throw new Renewing Mist and again to Tiger Stance. Few cycles should return you enough mana and provide you with some stacks of mana tea. Also you can cast Rushing Jade Wind from Tiger Stance right before you leave Tiger Stance.
It's even possible to heal like that with this rotation, and pull good hps, if you are crit+haste specced.
Bad thing about this way is that mistweaver in Tiger Stance tends to miss Jabs, which is frustrating.
Also you cannot really heal on reaction. If someone takes damage when you just used Jab in Tiger Stance, you'll need to wait for GCD of that Jab, then for GCD of switching Stance and only then you can start to heal player, who most likely will be dead already.
3. Spamming healing spheres under someone is quick and cheap way to lift his health up. Only problem is to seek where this player is staying. For that default keybinding Shift-V or Ctrl-V will show you hpbars of players around.
Healing spheres are great for healing someone, who needs healing in specific moments in specific place. It includes: blue Puddles on Immerseus; Imprison-ed players on Sha of Pride; tanks, when they pull bosses, especially on Dark Shamans; yourself before any damage spike. Precast them on the required point.
4. Using staff gives you more melee dps than using 1hand offhand. It's not apparent if you just switch weapons, but if you switch to staff, go Tiger Stance and back Serpent Stance, then you'll get your melee damage increased.
Mistweaver monk can create a lot of healing spheres before pull.
For that you will need gear with a lot of mastery, Glyph of Fortuitous Spheres and patience.
Make 2 equipment sets: first with your full gear, and second - without few pieces. When you switch this equipsets, you loose hp.
Now when you heal that lost hp, you have chance to summon sphere from Gift of the Serpent passive.
The simplest spell to heal yourself in this case is Healing Sphere.
With 30%+ mastery (of course, the more - the better) it will take around 2-3 minutes to cover big enough area with spheres.
Be careful and don't pull boss accidentally, if you put orbs around him
Based on Evermoon playing experience.