Omg thanks so much! Yeah, I've been using shazam and soundhound for the instrumentals, but also for the Korean songs because I don't know how to write the Korean words I hear (Korean spelling eludes me...). I also tried to use Naver Music, but it didn't really offer me up any results.
I've found that the creators were really funny and made a ton of references to other pop culture shows and movies. Speaking of which, there's a karaoke song when you get to episode 5 that I couldn't find. It's the second one they're singing, if you can transcribe the korean and look those lyrics up!