Your pet can do whatever it wants during Churning without damaging you.

The fight is fairly easy. I don't have a detailed strat handy to give you, but it's pretty intuitive. Shield/heal through tank busters and Ukehi, place fairy so that she can easily reach both sides of the split with Whispering Dawn, and keep up DoTs and Broil as filler while handling mechanics.

This is also an easier fight to use Aetherpact in since the tanks don't move often or very far.