I think the reason the gun did not work on the dragon was simply because it was a DRAGON, it’s just so big and it has a thick skin. Opening fire on a dragon seems to be the equivalent of a kid throwing pebbles at an adult, it’s annoying as hell but it’s gonna take a really long time and a truck load of pebbles before killing you.
When Emma will run out of bullet in is when will be the end of modern weapons in EF. Molotov cocktail are not exactly modern (alcohol burns… we did not just recently figure that out). I think Emma’s modern contribution on the battlefront in EF will be more on the defense side of things. Being a sherif comes with some sort of formation right? (riot police, how to properly immobilized someone with minimum danger to yourself… that kind of things)