Unfortunately there is no set answer, since the check engine or service engine light will illuminate for many different reasons, from minor to major problems. The best thing to do is to have you vehicle inspected by a qualified repair shop to determine the cause of the light illuminating.
Yes, this will cause a large leak in the fuel evaporation emission system, causing the light to come on. Simply install the fuel cap properly, after the computer determines there in no longer a malfunction for several ignition cycles, the computer will command the light off. If not it can be reset with the proper tools.
No, Preventive maintenance and service can be performed by your ASE certified automotive technician and maintain all manufacture warranties. The only service that must be performed by the Dealer is Manufacture Warranty repairs.
Most are an excellent investment, just be careful to buy one that allows you to have your vehicle repaired where you want to have it repaired. Also make sure that the company has been around for a while and has a good rating. Most warranty companies offer a premium plan that covers gaskets, fluids and many electrical repairs. These premium plans are by far the best value.