Seon Jae had already written the song by this time. Thats why it didn't stop.
I dont think Sol said about the past. The scene was in earlier previous episode was that she was talking to herself in her mind, not talking out loud. And she figured out by herself in her mind that Sunjae would tell her back that she is crazy. I think its the scene when Sunjae said a ghost can date too when she was trying to explain to Sunjae but realised that it would not make sense.
This drama is amazing. Applaud to director, scrtpt writer, production crew and actors. Watched three times and find it very relevant in IT field and also management field. No right or wrong but take into account of what gives less noise.