Here's what you need to know. Mist energy cannot be traded between players, either in person or through the Energy Depot. Also, you can never have more than 100 mist energy (although you can have extra tanks, that let you refill your 100 mist energy instantaneously). Other than that, mist energy and crystal energy are used for exactly the same tasks: crafting, running elevators, reviving, buying weapon slot upgrades, etc. And, whenever you use energy for any of those tasks, your mist energy gets used first, and then your crystal energy starts being used when you run out of mist energy. Now, for your questions:

1) what type of energy does the thing give? crystal or mist energy.

The Energy Depot gives you crystal energy.

2) if i had a full tank of mist energy(from daily) and i traded crowns for 100 energy..where would the energy go?

You would still have 100 mist energy. You would now have 100 crystal energy too, for a total of 200 energy.

3) if i had no mist energy (daily) and i bought the crowns for 100 energy thing. Does it refill my mist tank or does it add 100 to the Crystal energy tank?

It gives you 100 crystal energy, and it does not give you any mist energy.

In short, the Energy Depot is all about crystal energy, and has nothing to do with mist energy.