Most of this is from TMP conversation on 11/26/2022, with little bits filled in by me as I wrote this.
Contents
Students
Calendar Grithbreach
A "lore character", said to have been involved in the "Mastodon Incident" with ProfessorForneus. Was a student at Dame A's long before PrincessAlice was, somehow, even though Princess Alice is noted to have been a perpetual eighth-grader for as long as anyone at the school can remember.
Calendar now roams the grounds as a ghost. This might seem to imply that Calendar died as a child and on the school grounds, but we don't know that for sure--just that "they're here and child-shaped now." Princess Alice often hangs out in the ruins on the edge of the campus casually chatting with Calendar, seemingly unaware that she's talking with a ghost and not a fellow student.
Bunn E. Pumpkin
Like our friend Rabbit, but has orange hair with a little bit of green, like a pumpkin stem. Has a pet frog named Ptolemy who makes cute faces when things happen.
Bunny can't talk. They're the strong silent type!
Little Opal
Another student, a classmate of Princess Alice.
Melissa
An upperclasswoman, whom even the arrogant Princess respects as a senpai. May or may not be part of the weird dueling club that uses the Weird Staircase, but if she is, it's just because she likes anime too much.
Brick and Gutter
The "bullies" of Dame A's. They're not actually bullies and bear no ill will against their fellow students, but they've seen too many kids' shows with bully characters, and felt that someone needed to fulfill that role at that their school. They've been known to steal Bunny's Pokemon cards just because they feel like they're supposed to. Princess Alice attempts to stick up for Bunny, going to disproportionate measures like threatening to sic the CentraliaGuardForces on Brick and Gutter, but ultimately the day is saved by Calendar, who uses his ghostly ghostliness to spook the bullies into handing over the cards.
(The faculty often have to gently remind Princess Alice that she is a princess, not a dictator, and that threatening to turn her military on her own subjects is kind of a bad look for a head of state, even if she's like 13. It's the one time they encourage her to just tattle to the teacher instead!)
Locations
The Forest
A creepy wooded area next to the school grounds where students are forbidden to go, because every fictional boarding school needs one of these.
That Weird Staircase
A large spiral staircase somewhere in the remote area of the school grounds. Nobody knows where it goes, though some have said "I think they do fencing up there or something?" Some have noticed chanting that seems to be Japanese, though nobody is quite sure what "Japanese" even is.
The Computer Lab
An unremarkable computer lab straight out of a mundane 21st-century Earth school setting. Included mostly for the contrast with the fantastical nature of the rest of the school.
Other stuff
The Big Yellow School Bus
Dame A's has a single big yellow school bus. Princess Alice is forbidden to go near the bus under any circumstances, as the result of an unspecified incident. The incident happened long enough ago that even the Princess herself doesn't remember what it is. The police were apparently involved, but ConstablePayne refuses to share any details with the Princess out of fear that she'll say "that's so cool!" and try to do it again.
(As a side note, Constable Payne, it seems, is not an ordinary human, but the personification of the concept of law and order. Which, in addition to making her the natural antagonist of the Princess, a self-proclaimed agent of chaos, would also explain how she seemingly is able to show up anywhere and everywhere across all of Centralia and why nobody notices how strange that is.)
Because the Princess is banned from the bus, any time her class goes on a field trip, she must travel separately. She often uses this as an excuse to make a show by traveling to the museum or whatever in her own private limo, though the Headmistress has imposed some limits and refuses to allow the Princess to use the full royal motorcade for such trips. (Though the Princess does still travel with the full procession to and from school at the start and end of academic breaks.)
Bunny refuses to go near the bus because Bunny is allergic to buses, which are animals.
A bunch of stuff about buses being animals
I can't possibly be funnier than Sredni on this point so I'm just gonna copypaste it verbatim.
The legend of the doublehorse emerged from mistaken impressions derived from early sightings of feral pre-industrial buses, perytons and cameleopards. The modern bus is the descendant of the wild omnibus beast. Feral buses and wild omnibuses rarely assume a purely mechanical form; it is believed that the Catbus in Hayao Miyazaki's film My Neighbour Totoro was inspired by a rare Earth-side sighting of a feral bus.
Uniforms
Dame A's officially has uniforms, but enforcement of the dress code is fairly lax, so all the students have added their own little flair to the standard uniform.
Many students choose to personalize their uniforms with small brooches. Princess Alice, for example, has a brooch depicting the Centralian circled-star emblem symbolizing her sovereignty, while Bunny has a brooch depicting a bunny. The brooches are sold by "Big Bobby" Butterson (not to be confused with Bigbobby Butterson or Big Bobbie Butterson, who are different kids) from a shady briefcase in a dark alley--after all, they are technically a violation of the dress code, and that makes them contraband! Bobby can't risk the prefects finding out about her illicit brooch smuggling ring. Bobby also wants to avoid any conflict with a certain cookie supply sydnicate, with whom the prefects "have been forced to come to an uneasy truce due to past dress code violations and fear of the turf wars getting 'hot' again." (Sredni's words again)