In initial reports they said there are 2 doors, the main door which requires an electronic code, which the mum did not have, and the service door, which had the key in it. If there are two doors, it's very possible the service door always has the key in it. However if there are two doors it's also possible for someone to leave by the main one. I haven't had time to look for a better description of the apartment.
As for falling on the gun, that's very possible, also if they initially tried to open the bathroom door and found it blocked by the body they may have shifted things enough for everything to have moved slightly.
As for falling on the gun, that's very possible, also if they initially tried to open the bathroom door and found it blocked by the body they may have shifted things enough for everything to have moved slightly.