There are indeed limit adjuster screws on the front derailleur that can prevent the chain from falling off. You can do the job with a screwdriver and some patience. By the way, if the chain faills off of the large chainring, you can usually pedal and shift it back on without stopping.
There are good directions for adjusting the front derailleur limit screws here:
http://www.bikeforums.net/barnettes/barnetts_ch33.pdf
and here:
http://www.parktool.com/repair_help/...railleur.shtml
I don't know how mechanically adept you are. There are a number of possible causes for the "auto-shifting" you're experiencing. A worn chain, or worn cogs, or both are likely culprits. It might also be a stretched cable. I'd suggest going down to your local bike shop and having the mechanic look it over.