i wanted during runs listen to some songs

Yes, it's allowed. The rules say that "Audio is not needed, but is preferred". So try and make the main parts of the game listenable. The music should be lower down than the game.

Also can't you record audio only coming from the game? Rather than all of your computer's audio.

There is a resource on OBS studio called "Application Audio Capture" which you can find on latest versions of OBS, it allows you to choose which game you want to record the audio, even if you listen a music, your music will be not listenable on the video