"남자가 라디오를 들으면서 조용하게 노래해요."
Translation:The man sings quietly while listening to the radio.
Yes, but only the kind of "while" meaning two things happening at once.
Note that there is also a word 조용히 which is perfectly interchangable with 조용하게. Both mean 'quietly' and are derivered from 조용하다 - 'silent'
Because of the position of 들으면서 in the sentence, it has to be "while listening to the radio"
not necessarily, the actions are happening at the same time it should not matter which one comes first because it does not change the meaning
Probably there is no significant difference in meaning, but for learning purposes a and b and b and a should be distinguished.
"The man quietly sings while listening to the radio" was marked as incorrect.
"The man quietly sings while listening to the radio." is now accepted.
"While listening to the radio, the man quietly sings." is now accepted.