Looks like duels don't actually mean a lot and it was mainly the first prince that cleared them. The punishment is still a bit too light but that's just how things are. Actually the medal or promotion sounds really good ngl.
Well he is still the prince, and the problem wasn't how he treated Fine - it was that he somehow stole the state secret and still lost, making a laughingstock out of himself (and whole royal family by extrension), so punishment isn't exactly geared towards being fair to Ash/Fine, but actually fixing prince's attitude iMO.
Commoner actually being able to challenge a prince to a duel is kinda crazy too, but i guess their rewards are indeed very good - commoner girl gets a pension (HUGE for an orphan AND a girl in society probably without any safety nets - this is basically ensuring she'll have probably a minimum level of livehood covered), barely noble boy on the verge of becoming commoner himself gets to be a noble (and at higher rank too). On top of that, it kinda ensures the loyalty of them both (as both benefits are kinda tied to king being there), and costs the country basically nothing.
And with the revolution across the border, making the prince apologizing for being a dick might relieve some of the pressure that for sure would be building up in their country too.
We probably won't get it here, but Elise in this situation - if it was a bit more realistic - would have really serious problems. Forget the engagement being broken (existence of which is kinda unrealistic anyway), i'd expect her to be first interrogated on how she managed to get this sword, and then disposed of.