What is MacFUSE and do I need it?
MacFUSE is free software that lets you read and write Windows disks, as has already been explained. You do not need MacFUSE. It is not part of Parallels, and Parallels will work just fine without it.
2.0.3 is the current version of OS X 10.5.8; you can install it if you want to, or you can remove it by clicking on it in System Preferences and hitting the Remove MacFUSE button.