Not a suggestion with copying per-se but before you start to fill it up you might want to consider formatting it as Linux ext3 instead, since Fat32 only allows a maximum filesize of 4Gb. There is no such limit in ext3.
To run Linux on a machine with a Windows OS the simplest option is simply to boot it from what's known as a 'Linux Live CD' (or DVD) - free of course!. This doesn't install anything on your machine and doesn't effect Windows in any way, but allows you to temporarily run Linux. To return to Windows, just reboot without the disk in the machine. There are numerous Live CD downloads available around the internet, download, burn and boot! If you just want it for formatting disks then have a look at
http://www.finnix.org/ It's small and designed for admin tasks however it only provides a linux command line, so you would need to learn the appropriate commands for formatting a drive, see
http://www.cyberciti.biz/faq/linux-disk-format/