1. I really don't know the actual name of the puppet used. Phil used "Big Head" as the name for the banner in which he appeared in (in the Muppet Meeting Film, he had short black hair and a grey suit). I like the addition of "Fat Valkyrie" since she made two appearances: once during the "Noses" song, and in episode 4081 (she sang "la-la-la-laaaa" during the song about all of the different ways people communicate).
2. I'm not really into Eminem, so I can't answer that. Hopefully someone else can help you with that. In the meantime, keep him in the "Phlegminem" category.
3. The bully named Peeno was a completely different monster; I believe I gave a description of him to you (yellow with horns and a dark pink nose).
BTW, I just wanted you to know that on your list, "Tony and Maria" from "Inside, Outside Story" are listed as monsters. They're not monsters; they're both Anything Muppets.
And the saxophone player from Bruce Stringbean and the S Street Band is named C-L-A-R-I-C-E, not "Clyde" or "Clarence".
As for "Elmo's World", The Sun is basically an orange sun with rays sticking out. She had a big smile and round white eyes. The Moon is round with a half-moon shape on its left side. The "moon shape" has a nose, while the other side is a dark, starry sky, and the entire puppet has a black mouth and dark sleepy eyelids.