Traits and stats don't do anything to progress the story. They just unlock more of that content, as the game sees you enjoy that content.
To advance Kali's level, click on her door in the morning.
Ah, yes-sorry I didn't indicate better, I've tried that every day of the week. Every morning the only option is "Knock on Door" except :
Sat-she's showering
Monday- she's in lobby
Wed - she's in the hallway next to shower
You may be experiencing a very old bug from a save that is years old. When was the last time you played this save? The easiest solution, though not the only solution, is to restart your save. Which I highly recommend with v0.18
Cool-Ill wait a while and restart later-great game, BTW!