ok, i am by no means a mac expert, so part of this is based on hunches-- if there is any way to contact the original owner for help, it would probably be for the best..
1)i 'think' that the mac mini is a intel based system, meaning that i think that it should be able to run any windows OS. my opinion on xp, vista and win7 is dramatically different--
xp is the smallest, taking up about 5gb of space on a full install, it will work, but is a more then 5 year old operating system, so support is starting to run thin.
vista, is junk, plain and simple, it will sometimes work for some, but has the typical windows 'new OS' birthing issues... it is also around 15gb on a full install..
win7, i have been very impressed with-- i am now deploying win7 systems at work with almost no problems(we never deployed vista systems--too many problems, and most of the current problems involve the small differences in setup between xp, and win7), and have re-done my gaming system, and car pc with win7, and my new laptop includes it. it is also slightly smaller then vista-- coming in at about 10gb of install space.
win7 also seems to boot a little faster then xp, but it might be my imaginiation-- i haven't really tested it..
2) this could be due to a poor/corrupted file/OS install, or too many files--when my computers get to that point, i backup my important files, and reinstall the OS-- it is the only way that i can guarantee that i won't have a problem later...
3)i think that wire is for connecting the power supply to the power button of the mac-- to allow the power supply to turn the pc on and off, depending on the ignition position.
4)i am by no means a expert on fe's(i consider my self lucky to get them to work at all), but i believe there is a way to setup a button in either to do as you want