"should I update the older computer to Windows XP before I set it all up? Or is Windows XP even compatible with a 500 Mhz computer?"


Xp will run on the specs you offer but a visit to the Compatibility website may be worth it. http://www.microsoft.com/windowsxp/pro/upgrading/advisor.mspx

"Does the fact that the two computers have different operating systems going to affect anything??"

For most things no.

"Will we be allowed to share files through this network too?"

Absolutely.