When I try to change language settings in Settings app I can't do anything, it first asks me for password to unlock all of the features, and after that i can't change anything. I hope you can help me, I'm using Elementary OS 0.4.1
I had the same problem, it's already answered on this link: Languages won't show up
But just to save you some "work", you can get the solution by clicking the "+" button on the bottom of the left sidebar, then all possible languages will show up.
Ah, I have a question for you, what's the theme you're using?