1. It records the driver records. You set how long you want the device to "remember" the driver by setting the "Enable driver identification reminder" to a length of time you want the device to "assume" the same driver is driving the vehicle. Otherwise the driver should be "Unknown".
2. No it does not work that way. You need to define "forget" in your terms. The data is always kept for records.
It sounds like you are mixing up your information. I get the impression you are referring to the Map showing you who is "logged" into a device. In that case the Map will routinely show you who last logged into the device even though they are not currently in the device.