The guy at the shrine that requires you to be "Smart" is the Sun Arcana. He is only available on Sundays.

The Gourmet at the mall who asks the annoying questions is the Moon Arcana (Level him up, Moon is pretty good)

The Monk at the Night Club is the Tower Arcana

The Head of the Disciplinary Committee is Emperor

Hama and Mudo are really annoying but to be honest, it's been considerably powered down from one of the main MegaTen games. If you've finished the Death Arcana then I advise creating Thanatos to counter Mudo. To make him, you have to do a Petagram Fusion with all the Death Arcana Persona. He's really good and can easily carry you until you acquire one of the end game Persona.

I can answer any other questions if you have any. Chaos, I think you are a little underleveled (what month are you on?) the easiest way to level up is to find the Shadows that are a flashing pinkish red color. They tend to be uber high level monsters but they'll level you quickly. I also advice you to find the Growth abilities for your Persona and keep them as you fuse them. Growth lets in-active Persona gain experience. 1/4 for Growth 1, 1/2 for growth 2, and full experience for Growth 3.

I also cannot stress how important it is to finish all of Elizabeth's requests. Especially the ones without time limits. She gives you some really useful accessories and the Fusion challenges net you special items you need to create special fusions like Alice and Black Frost...