I'm not sure about the answer to your first question, but keep in mind the inactivity does not equal idle time. I believe idle is measurement since the last time a record was committed. You could have a user actively working in a file but the server thinks they are idle. An example of these might be a user typing a lot of text in a large text field . They could type for an hour in this field but still be considered idle if no commit occurred.
I'm asking this because I would like to accomplish something like the following. For people that have only one open database solution running, I'd like to be able to close that upon prolonged inactivity, and quit their local occurrence of the FileMaker client application. Other people might have a second database solution active, and for those I'd like to be able to just close one of them, without quitting their local FileMaker client application, keeping their second database solution "alive". Gee, how stuff like this is sometimes hard to explain; I hope you get the idea.
What you're describing could only be accomplished from the client side. There's no functionality in the Server application to force-quit just a single database automatically. (You can do it manually, but that doesn't help you.)
To accomplish the task client-side, you could run an OnTimer script on each client that monitored for activity and then performed the action you wanted. See this recent related thread for some discussion:
Edit: Note that none of this interacts in any way with the server. If you set the server to disconnect after a certain idle period, it will still kill the entire client, regardless.