Thank you so much! The "Password Protected" sidequest is only available inside the first dungeon of chapter 2.
I'll take a look at that bug you mentioned about the "Lost Key" sidequest, because that definitely sounds like a bug. The quest completed notification usually pops up as soon as you open the door (which means it could be misseable since it shows up during the transition). Inside the pause menu, does that quest show it's 100% completed?
In any case, thank you so much for taking the time to report it! Hope you have a great day!