The WD support requires the drive's serial number be entered on their support page's request seen there. All the zip file is are the files that come preinstalled on the drive where the unpack to the drive replaces anything missing like the autorun.inf file. That goes quick once you have the download and simply extract the files from the download onto the drive.
For working without full administrative access you would have to go to someone above you in charge there since that's not your own private property. And no it only replaces the original program not wiping anything else leaving the partition intact.
With an NTFS NT cored OS the idea of first backing all files up and reformatting to NTFS and then extracting the original software files to the drive is the best move for Windows. XP and Vista alike will then readily see the drive just like it was an internal model while you can still run the installer. Fat type partitions require the software so that the newer versions can see onto that partition type as well as being compatible for Mac. That's why you see the Windows/Mac compatibilty seen when first buying one.
Even the support site at Seagate for that brand recommends first reformatting to NTFS if Windows is the OS to be used. Sometimes the Fat32 factory partition doesn't go on fully and results in problems like the one you are seeing now. I ran into that here where once I saw Fat32 was the type I backed up everything and simply reformatted the drive.
WD's support page is seen at Downloads
Once there you have to select the exact model following the My Book title with Essential, Essential 2.0, Home Edition, Office Edition, Premium, Premium ES, etc. there or enter the model number. That will take you through the process where the actual serial number for that particular drive will have to be entered to be able to download the replacement in a zip file. The information there will instruct you to simply unpack the files onto the drive itself.