Yes, first one is a distorted version of "Mad Hat" (Count Cannoli battle) from Wario Master of Disguise by Kenji Hikita. No idea about the second one, never heard it.
The music at 7:35 actually starts at 7:16. It's also used in the introduction for all 4 episodes. As for what it's called, I also have no idea. It could just be a random piece of music especially made for the videos.
And I have searched ALL FOUR videos for any comments containing the words "music", "song", etc. Nothing. There is a comment saying asking about the tune in question, but of course, this is YouTube, where people can ask the name of a song, and still not get a reply sometimes YEARS later.