Welcome to JustAnswer.com! My name is DriveFast71(Ron) and I will do my best to answer all of your questions completely and accurately.
When the Check Fuel Cap light comes on, this can mean more than "just" a faulty Fuel Cap. When this is the case, the Check Engine Light is usually close behind. This is a sign that there is a problem in the EVAP (emissions control) system. Unfortunately, there are literally dozens of parts/sensors in the EVAP system that, when faulty, can set these lights. The only way to get our starting point, is to have the "p-codes" (diagnostic trouble codes) retrieved from the on-board computer. Most local "big chain" parts store (like AutoZone) will read these codes for Free (except in CA). Once you have these p-codes, you now have a starting point and can more accurately and efficiently diagnose the problem, and then make the repair. Very commonly, this is a problem in a solenoid or valve in the system, but again, we'll need to know which one, as replacing parts at random will get very expensive and fustrating very quickly.