Beatrice is in High hall, up hill from the merchant guy.
Hint: mind read her and call her out on what you learn, you'll get a bonus for doing her quest then.
Was that key in a house that no one is around, like deserted.
Look around in that house and see if maybe there is not a box/case up on as shelf that the key is used for.
Can't find anything on that key in any of the walkthroughs I've looked at. I broke every vase and box in the game I saw so I probably found it but what it's for I can't say as I don't remember it.