My fiancé does not have a computer. He has a first generation iPad, which needs to be updated, but can only do so by way of iTunes on a computer. Can he use mine? How would he go about creating his own account on my computer?

A first generation iPad is unlikely to have any new updates. It should be running iOS 6.1.6 which was released 4 years ago. You can potentially connect it to your computer to update using iTunes if there really is an update available. You can also backup the device. Simply updating a device should be OK, but see View and remove your associated devices in iTunes - Apple Support for reasons why managing devices across multiple Apple IDs isn't quite so straightforward. Accessing past purchases from one account can lock you out of another for 90 days.

tt2

I consider turingtest2 the guru of iTunes for Windows and I would follow his advice closely. However, if you really want to set-up iTunes for multiple accounts, this (outdated) article may help:

How to use multiple iPhone, iPad, or iPod devices with one computer - Apple Support