In the prologue Crowley declares that Grim and the prefect are allowed to live in Ramshackle for free, but they will need to pay for their own food, clothing and incidentals.
It seems the prefect has no money on them with which to do so, so Crowley hires them as janitorial staff.
(The scene above is almost identical in the novel, with the addition of, “Your wages, well, you will be compensated fairly according to the nature of your work.”)
What the game is vague about is whether or not the prefect and Grim are monetarily compensated for their work, or if they are just working in exchange for meals and clothes.
But they do seem to have money from somewhere, purchasing various souvenirs for themselves and others throughout events, so it might not be impossible?
Trein has a line of, “You must be judicious with the funds the headmage gave you,” but we do not technically know if they received money only for Glorious Masquerade or if he is referencing money that they receive from Crowley regularly.
The novels do answer this question, but the novels will sometimes change details from game (i.e. the retconning of Leona’s introduction, the addition of multiple new scenes, etc.), so while it might be ok to use them as a reference, we cannot emphatically say, “this is how it is in the novels, so the game must be the same.”
The second novel begins with Yuuya, Ace and Deuce making repairs to Ramshackle, and Yuuya later compensates Ace and Deuce for their help, in cash, by buying them pastries on Bakery Day in the cafeteria:
“In response, Ace and Deuce smile as they place several white packages on the table. Here and there Yuuya can see thick slices of roast beef and vibrant green lettuce. There are round breads bursting with cream, baguettes topped with melted cheese, and more—it seems they were able to buy quite a considerable amount.
But they still have change leftover, which they pass to Yuuya, so the prices must be student friendly. It makes sense that bakery days are so popular.
Still smiling, Ace and Deuce sit across from Yuuya.
‘Thanks for the food!’
‘Gonna dig right in!’
‘Of course. Thanks for helping with the repairs to Ramshackle.’”
-Twisted Wonderland the Second Novel
So novel-prefect is being paid in cash, and seems to be budgeting accordingly. This is particularly significant because it happens in Book 2, after the prefect and Grim have transitioned from janitors to students. While their roles are different, it seems they are still being paid for repairs they make.
And this might be also happening in the game, although it is possibly never acknowledged aloud, with Ramshackle Dorm getting cleaned up between the Prologue and Book 5 (presumably because of the prefect and Grim working to earn their food and clothes etc.)
An argument against this theory might be Grim’s line about not being a part of janitorial staff anymore in Book 2, but while novel-Grim is also no longer janitorial staff by Book 2, he is still helping with repairs, so this comment might not be applicable.
Mostro Lounge (and the school store) would probably not be as successful if they were competing with free cafeteria food, so it is possible that the other students at the school are also following the system that the prefect uses (free lodging only).
This would explain why Ruggie does things like wear Leona’s clothes and eat wild plants: it is possible that he showed up without any money at all and is making things work day to day, exactly like the prefect.
Crowley will occasionally threaten the prefect and Grim with how they’re racking up expenses that he has never agreed to cover, which might mean that game-prefect is living at least partially on credit, charging expenses to Crowley or the school?
(Which is something we know the school store can do based on Azul charging costs for cleanup of a mess made by Jack to Leona.)
On the subject of tuition, it has also never technically been officially confirmed or disproved that scholarships or tuition are things that exist.
The is fandom discourse that NRC is likely a private school that operates on donations and does not charge tuition, and Crowley does mention receiving donations from parents, but it has possibly never been stated outright in the game (or novels) and may just be conjecture at this time.
To answer the initial question: Maybe!
We know Novel-prefect has money that they are receiving from somewhere, presumably Crowley, and we know Game-prefect is also receiving money from Crowley, but whether the cash they are being given is only for field trips or is something they are earning through repairs to Ramshackle is unconfirmed.
It is possibly one of the many things that the game is intentionally keeping vague.
Twisted Wonderland Reference Note 