Get ready, gonna blow you guys out of the water.
1 Bean Bunny did appear on Muppet Babies, wearing a darker jacket than his normal puppet version. He also had these clearly defined eyes, like Piggy's, not beady little eyes.
He appeared on the later seasons, once they switched to the newer intro segments.
2 Toddler Janice did appear in only one episode. This was an episode with Bean Bunny as well, who was recognized by Toddler Janice because they saw each other at the center she would go to. The plot of the episode was that Bean wanted someone to read him his favorite story, the tale of Peter Cottontail. Janice said that she could read, to which the others were a bit amazed. Naturally Piggy became jealous and pretended she could read as well, when she couldn't. The funny part was seeing Piggy and Janice battle it out between each other as Mother Rabbit in the fantasy segments of the episode.
3 Robin did appear from about the second season onwards. He appeared as a tadpole in his water-filled glass bowl. He had two forms of talking: baby gibberish to most everyone else, and a baby-sounding normal internal thought voice. Robin and Animal formed a cute duo in the later season episodes.
4 Statler and Waldorf appeared in the later seasons, in their adult form much like the Palisades figures. They were brought in as the babies' uncles, most probably to get these two recognizable characters into the show.
5 Camilla was a stuffed chicken in the regular segments, but she came alive in the fantasy segments.
6 Baby Skeeter. There have been puppet sightings of this character in Muppet Babies nursery rhyme books and/or calendars. There's also a sighting of her behind the stairs in the home movies segment of MFC, but I'm not entirely sure on that one.
Agree that Karen Prell would be a good choice to voice Skeeter in either baby or adult form.
Hope this helps and have a good day.