I will try to add my own reasoning behind the pros and cons of such a city/village. I've read and thought about your answers and comments, and that brought even more food to the table. I'll try to add all the current answers to the process in order to provide viewers (and people who want to set up this kind of city/village) with the most complete answer possible.
How it holds together
Short network with no master
First of all, dario quint's answer depicts one detail that would make the system work. With a small scale village, everyone knows each other, so you would be "peer pressured" to work together in harmony. As he points out, if you know and trust other villagers about your needs (e.g. I need clothing from the tailor, and the tailor needs my fruits to cook for his family), your goods turns out to be needed by everyone else, thus letting you with a low oversupply and an ability to trade with everyone about what you need personaly. We'll come back in the second section about the drawbacks of such approach (human nature and/or living in autarky being quirky).
The second positive answer comes from Ash and sheds light on a fair amount of possibilites about how could this city/village may survive. The benevolent nature of the leader solves a lot of problem, especially the one about money being needed as a trade: if you live under a fair leader which provides you with everything you need, then money is of no concern because you work purposefully for the community under your lord's lead (not ownership, they are not slaves). The lord itself may have his reason to act so (ancient family curse, special spell he fears, fear of a judgment by a higher power).
Why it cannot be (without adjustments)
My fair share of lazyness and ignorance
A lot of comments pointed out incoherences, plotholes and/or straight missing points about the whole setup. A medieval fantasy setting means a 500-ish village clearly cannot supply itself in food, and if it can, it cannot support a college/university as planned. Money came way later than cities, which means we already have live examples of such places. Gunpowder is a threat even with the magic system, because it got found way before and could still be as destructive, if not more. I did not search the whole array of possibilites before asking the question. That one's on me.
The outside world does not need it
If your village/city is living on its own, without money, well, first of all that'd a huge city considering all the raw materials needed to survive in autarky. Second of all, what would be its purpose to the world ? Is your city/village bringing something to the outside world ? If not, think about it, because that's a key point. John pointed me out to a
great resource about Urbino, which survived solely on the money of one man and brought to Italy the greatest mercenaries in Europe. He brought something to the world that allowed its city to live peacefully (and even expand). For my case, the university is definitely a point I'd want to rise in order to provide the surrounding city freedom.
The nature of men
By nature, humanity sounds encline to strive for more, or at least shows a distate for staleness and non-improvement. No sane human would want to live its all life doing one single task (let's say, wood chopper), without expecting any improvements or changes in its life. Or maybe only a few, in my opinion. What would drive people to work for others ? Can you really bring between 300 and 1000 people sharing the overwhelming passion for caring for each other in one city and expect it to live throught time without corruption and madness ? That's a second important point I've read and thought about: how is your city surviving through time, and how its inhabitants live the staleness ? And if they don't, how is your city improving ?
The world is huge
Bryan McClure highlights in his answer a point about foreign goods. Without money, what brings the rest of the world to your city ? Can your citizen taste/see goods from around the world ? Imagine your could never taste a dragon fruit or have a computer because you live in France and have no means to grow such fruits or mine the necessary materials to build a microprocessor ! In a medieval setup, if your region has no fruit, so no one could have fruit without a mean of interacting with the outside world. And if the outside world uses money, you have to bring something to the table for it (see point above).
300 people is nowhere near enough, in a medieval fantasy setting, to bring food AND supply to everyone in this city. As a lot of people pointed out, overproduction of food was not a thing with that scale of town. It may be if around 250+ people were farmers / hunters, and that is not the case (there's a college, after all). So maybe change the scale for something bigger, but in that case, how is a 3000-ish city/big village working without money or someone to govern them ? Read about food production in pre-modern world and you'll quickly see a lot of holes in a simple setup, simply because history showed us.
To conclude: I don't think a village of 300, or even 500 people, can survive considering the current setup (university, magic using scrolls, no money inside the city). To make it work, consider the following key points:
- Your village/city have to bring something unique or valuable to the world, otherwise it will be conquered and/or wiped out easily by side lands (war is war, especially in medieval times).
- If you plan on supporting a big entity (university, corporation, etc), change the scale. You need a way bigger city, or you need a mean to produce massively for less (food especially).
- Think thoroughly about the relation between material goods (food, clothes, jewelry, furnitures ...) and services (protection, administration, justice ...). Even inside the Material group, think about the relation between essential and non-essential.
- Don't forget that, eventually, men will try to take power and/or break the monotony at some point.
Thank you to everyone that participated in that exchange, that helped me a lot !