Conical bullets were invented in 1832, and were widespread by the time of the American Civil War. As for the gun, it's looks closer to a percussion cap than a truly vintage flintlock. But at the same time the multiple bullets means you can disregard the assumption of it being a muzzle loaded...
My personal theory is the boy she's been crushing on is also a FtM, and this is a fulfillment of her early chapter wish to "have something in common with him."
Well, hopefully I'm reading it right, and the King literally bribed the FMC to not enroll at the same time as his daughter (the princess), probably as a way of her being able to go to school without being in the FMC's academic shadow, so now when they enroll, she'll have graduated, and avoid the...
Now I need that Isekai. "I Reincarnated in a Dating Sim as the Villainous System, So Now I'll Change the Genre and Ship All The Girls With Each Other For The Readers!"
Magic continuing to advance is a nice setting tool. Early on we got introduced to the demon sage that created Soul Track, and how that revolutionized magic, and now we get to see what magic used to be, and the regrets about it's limitations.
And then of course we get that brief glimpse of the...