"we listen to radio" is a perfectly natural sentence. in this context, radio means not the object, but the programs or music that are being broadcast.
"Do you listen to CD's in the car?"
"No, I listen to radio."
How to say ' we are listening to the radio'?
I say "we listen to radio" or it could be "we listen to the radio" . Not exclusively a radio. A.
I think both "a" and "the" should be accepted although "the" is more common, but "We listen to radio" is wrong.
I've seen ця for use with feminine nouns. But I'm not familiar with цю. When is it usually used?
Цю is the accusative form of ця.
Ця машина моя (Nom)
Я маю цю машину. (Acc.)
Цій машині три роки. (Dat.)
and so on, just like Latin...
This pronoun varies depending on the genus. In this case- indicatory pronoun (вказівний займенник) http://pravila-uk-mova.com.ua/index/zajmennik/0-13