Fast user switching is a way of quickly moving between accounts, by leaving one account running in the background. If you always use the Apple menu, then that's not the case, so you don't have to worry about peer-to-peer (those are file-sharing programs, where people can trade things like music and movies).
you've got 2 gb of memory, which is on the low side for Lion (assuming you're using Lion). That can cause excess disk usage (and thus excess heat) because the system will be paging memory out to disk more frequently. It would be worth the $100 (or whatever) to buy a couple more gigs of ram - when I did that with my laptop the difference in performance was noteworthy. If you tell me which model MBP you have I can link you to the correct memory type and tell you how to install it.
Do your kids have standard accounts or administrator accounts? You can check that in System Preferences -> Users and Groups (that used to be called Accounts, if you're on an earlier system). You should set your kids to standard accounts if they aren't already, which will keep them from innocently installing something like MacDefender.
Did Force Quitting Skype solve the fan problem?