1) Not possible without 3rd party software.
2) Unless there's something special going on, the user's maps are to a shared folder, and not the root of the drive. Therefore, it doesn't matter where the files reside on the server, the clients map to the share name. (i.e. \\server\share)
The drive letter on the server has nothing to do with the drive letter of the map on the clients.
It should not be a problem to move the entire shared folder from the F: to the G:, then re-create the folder share. If done afterhours, it should be transparent to the users. Their maps will still be to the same data, but on the G: drive instead of the F: drive. However, on their machines, it will still map to the F: drive letter.