The Muppets have made many appearances on The Tonight Show. The first appearance by The Muppets on The Tonight Show was when Steve Allen hosted. I have read that grover once appeared on The Tonight Show doing near and Far with Johnny Carson. During the opening clip montage in Great Performances: The World of Jim Henson, there was a clip of kermit and fozzie with Johnny Carson.
Regarding a ten minute opening monologue, I have seen clips of kermit doing a monologue from the night that he guest hosted. It could be ten minutes, and it could have been to open the show. These clips were in The Muppets: A Celebration of Thirty Years and The World of Jim Henson. At times Fozzie appeared from behind the curtaisn and made some comments, such as "louder and funnier" and "you're dying".
I know that, besides Kermit and Fozzie, that epsiode featured Miss Piggy, Gonzo, Camillia, Uncle Deadley, and The Electric Mayhem (I think all five original members, but I'm not sure). Did any other Muppets appear in that episode?