It is perfectly ok to say that "She never listens to radio" it does not need an article like "THE". "The radio" is refering to a specific radio, whilst "radio" could be any radio.(She never listens to singing birds ". /"She never listens to the singing birds")
American English tends to require the article in places that British English does not, such as "the hospital" instead of just "hospital". It sounds strange, possibly a bit archaic, to not have 'the' in American English in this case of "the radio' vs 'radio', but it is not objectively wrong. Just not the way it is used standard in the US.
It says "radio" here, not "radion", so why does it require definite article?
Because in English, that's just the common way to say it. The same goes for the Internet, which also will require the definite article. Swedish does not, however, use the definite forms and that's why this sentence is a correct translation.
Is there any way in English to separate never listening to a radio broadcast and never listening to a radio receiver?
In Swedish the sentence "Hon lyssnar aldrig på radio." Means she never listens to any radio broadcast. "Hon lyssnar inte på radion" means "She never pay attention to the radio receiver." (She could have it on in the background, but not listening to it.)
It would probably be more used in a construct like: "Stäng av radion om du inte lyssnar på den." - "Turn of the radio if you aren't listening to it."
Possibly. A distinction might be felt between "She never listens to the radio" and "She is never listening to the radio", the latter might be more likely to indicate that the radio is on and she is not paying attention, but mostly the distinction is solidified through further explanation than inherent in the phrase.
Nonetheless, I am not sure it would be a mistake to say "She never listens to radio".