Hi there!
Thank you so much for playing the game, I hope you have been enjoying it so far.
So technically speaking if your Companion used up all their EP then they would become unconscious and it’s up to your squishy character or another companion to try to wake them up. That said, if that feels too ridiculous (my mighty companion tried to open a door too hard and fainted 😅), you are 100% free to narrative your way out of that issue.
Likewise with the door situation: if you’re out of EP and your luck rolls have failed (and you haven’t learned any Passwords yet), I like your resolution of having the complication be the door falling on you or a companion (best be the companion who can lose some HP, as your squishy character would have to successfully luck roll a dodge or instantly get… well, squished.)
I hope that’s helped! At the end of the day it’s your narrative to tell so you’re free to tweak things as much as you need to ensure it feels right for you ☺️