As a new player, I have a few questions related to quickcast actions.

Basically, during some games as the beastmaster, I will (before activating my creature) quickcast Battle Fury on my Steelclaw Grizzly in order to full attack and then quick attack. (In these instances, my creature and my opponent share a square before I quickcasted Battle Fury) Then, in response to my quickcast, my opponent will quickcast a Teleport to be out of range of my creature.

My questions are:

Would a quickcast reaction possible in a situation like this?

If yes, would initiative and/or creature ownership effect the order of quickcast reactions (before creature activation)?