You can use "/sbin/udevadm info --query=property --name /dev/<device>" to print information about a device.
If you know the node, also look at "ls /dev/disk/by-uuid/* -l" or "ls /dev/disk/by-path/* -l". These will be symbolic links to the actual devices and contain the path or uuid in their name.
Using policy kit, you can disable the users ability to mount external drives all together.
You could also have an /etc/fstab entry for mounting a particular usb drives filesystem with "uid=" and/or "dmask" options that will only give access to a particular user. This will only work on that computer. If the user can use "sudo" or "su", then all bets are off.
For your own program, you would probably be working with policy kit to enforce your own policies.
Here is an overview about how policy kit works.