the exams is not something that you can savescum. at the start of the week it rolls the value from 1 to 100 that your skill has to surpass. you can luck out or get a high gate, but it happens way in advance of the actual exams so savescummers can suffer.
Learned something new! I figured it was set sometime in advance, but exactly when was opaque. Good to know, though.
Why are recipes valuable though? Never had any need to use any of them yet.
Also, is there any place to get clothes besides the clothing shop in the shopping centre? Got caught stealing there a few times, now it's unavailable during the day and during the night there's always a guard and no way around them. Or alternatively, is there any way to mend damaged clothes or prevent them from being destroyed?
I don't think there are too many recipes with high value, though I suppose for a new player you could potentially luck out and get a decent recipe that's easy to make and relatively high value to sell at the stall? I feel like probability of that is pretty low, especially if you aren't playing DoLP, but I'm pretty sure even something like porridge is at least more valuable time/effort-wise than some of the other low-paying jobs (chalets, early cafe) and comes with the added bonus of having zero potential for harassment while making them, AFAIK. Hardly amazing, but would get you through the first week, maybe? Though so far I feel like food is mostly for love interest interactions.
As for the clothes, the tailor can fix clothes (assuming you can still access?), and if you had turned on the auto-buy option before getting barred you might(?) still auto-buy destroyed clothes despite not being able to go in the shop, maybe. Aside from that, in terms of shops I can think of the forest shop, the school library, and the Gingham clothes that sometimes come up when looking through the market stalls. Other sources include Leighton (showing up to school in non-school attire), Morgan (not ideal, but sometimes dresses you in starter clothes), the random encounter with the bimbo clothes, and the catsuit from the docks. Not an exhaustive list, but at least some of the more easily accessed ones, anyway.
Ed: Just tested the exams thing - there might be a set roll for the standard tests, but at least as of current version (0.5.4.4) you
can manipulate RNG for the Housekeeping exam on Thursday. I had different recipes come up as a result of trying different actions, some of which I could pass, and some of which I failed (@ only a ~50% pass chance).