I know you can get essence from the diamond shop, but where else?

Plus I'm facing the boss of fungus grove, and he keeps knocking me out before i can do anything about it.

Places to get essences other than the diamond shop:
-trade broker
-nurturing (very rare)
-battling (rare)
-opening mission satchels (rare)
-Jinxie's Jamboree (rare)

As for your pets passing out... either they need to be higher levels, need better armour, or you need to look at how you have their stat points allocated. Here is a guide to getting your pets ready for battle.

Hope that helps!