Proč je na konci to "to"?
Protoze LISTEN TO je "poslouchat ..neco"
I am listening TO music.
Can you use it the same english does to ask "what kind of music do you like listening to?"
To what are you listening?
Quite grammatically correct! But it would be used very rarely, at least in the US. It would pretty much universally be, "What are you listening to?"
the word to is not neccesary in that sentence
Assuming you're referring to the English sentence, "to" is indeed necessary. "What are you listening?" is incorrect.
It would be unusual in the US to have that sentence end without the "to." 'Course in England, ending a sentence with a preposition is something up with which they would not put. (Winston Churchill) ;-)