Is radio a plural for some reason or does sluchat' take the genitive?
What is the different between "is listening to" and "is listen to" in this case?
"is listen to" is not proper English. Either "is listening to" or "listens to" would be appropriate. The first is talking about a current, ongoing action, while the second is usually describing a repeated action. For instance, if I say my mom is listening to the radio, I am probably telling you why she isn't with us in the kitchen right now or something. If I say my mom listens to the radio, I am talking about a habit of hers, maybe indicating that's how she gets the news, instead of the television or newspaper.
Stupid is as stupid does and I've done this dozens of times. Not paying attention to what I'm doing. Too much concentration on typing.
Isn't "radio" neutral? I thought that neutral words do not change in grammar cases. Or maybe would both "radio" and "radia" be correct here?
"radio" used to stay unchanged in every case a few decades ago, now it's considered dated.
But anyway, see what Vengir wrote.
Neuter words also inflect by case. There are some words that don't inflect at all (for example the -um words in singular or female names that don't end with -a), but it's separate from their gender.