Can I play Look What I Found! at a location with a Locked Door attached? Can't seem to get a straight answer from searching the web.

I am going to say no. Locations with Locked Door 'cannot be investigated'. Look What I found is only triggered by failing an investigation check...which you can't do with a Locked Door in place.

In general no, but I think there are a few edge cases where you are at one location but investigating another, like with In The Know . If you were on a location with a locked door and you investigated another with In The Know and failed, I think that you could play LWIF to discover 2 clues on your location.