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Yes, the computers stay on the DHCP list even after they are no longer connected. I'm not sure exactly how long, but it probably has something to do with the DHCP lease time.
As dilbert mentioned, the fourth computer you are wondering about could be your computer if you connected both wired and wirelessly with your laptop. Each network card has a unique mac address, so your wired and wireless network cards will show up as two separate entities.
I'm not sure about monitoring network activity. I know my router has basic logging capabilities, so I can see a list of all the sites that have been accessed over a certain time period. You could check your router to see if it has anything like that.
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