An aid to sneaking through Calcelmo’s Laboratory is to use the various traps in the area. If used properly, all guards can be neutralized without getting a bounty. The Shout Throw Voice in combination with sneaking can prove useful if the Dragonborn chooses not to eliminate the guards.
Keeping the crown The Jagged Crown could be kept by reverse-pickpocketing it to either Hadvar or Ralof after the crown is collected but before the quest is completed. It is still important to keep backup saves, though, to ensure that Hadvar or Ralof do not disappear after the betrayal.
Kill and loot the Falmer Gloomlurker (he has the focusing crystal you’ll need BEFORE you speak to Paratus Decimus, otherwise the game will glitch) then go to the right path. You’ll go through a few doors (there are no enemies) and eventually you’ll see a chest up on a shelf directly infront of you. The key is in there.
Where is the key for Mzulft Aedrome in Skyrim?