There's nothing to "do" with the radio - it's worldbuilding and lore and will come into play later. "Hints" were for increasing the love level of each of the girls, and that's redundant right now, with only one love level for them remaining and no way to get the last heart right now (if I put anything in the Hints people would think there was a way to get the last heart).
Viewing post in PUBLIC RELEASE - v0.20.2 - KANA COME HOME! comments
Ah, yeah - because the main storyline at this point is "conquer territories, stop the war" :) Side quests are taking a back seat until MC is more comfortable with his tactical position.
Leads will begin to pop back up again as MC conquers more locations and gains access to new events, lore and answers to certain mysteries.