Welcome to the message board Boss! I will answer your questions the way I see them.
1) You don't need camo, but I wear it just in case. I also wear gloves along with my facemask which I use for Turkey also.
2) The .22 will work great, especially with high velocity varmint rounds.
3) I try and skin the squirrels as early as possible. They are super easy to skin when they are warm. When they turn cold, it is much harder around the ears and face, much harder than it would have been if it was warm.
4) It really smells when you pull the entrails out of the animal. But then again, so does every other animal!
Good Luck. There should be plenty of people on here from Illinois that can help you out.
Joe