How you ever danced ecstatically? Like gone crazy while wearing headphones or something?
I have not, but I do know that it was first used in 2001
What is ecstatic dance more precisely? I assumed it was just flipping around like crazy.
Sort of.  It is considered transcendental and sacred dance that consists of movement meditation
Is it tied to a specific religion? Or is ecstatic dance just more of a generally spiritual thing?
I do not think it revolves around a particular religion.  It is open to all and is drug and alcohol free
I sort of sounds like yoga but hyped up instead of chilled out. Any connections to yoga practices?
Not that I am aware of.  I do know that yoga has a variety of practices 
Where is this dance done? Is it a gym thing or is it done at spiritual centers or something similar?
It actually does have a specific place.  There are no guidelines or a single format that it consists of