Here are your answers:
1.) Probability of precipitation refers to the chance that a certain point will receive measurable precipitation. It does not have anything to do with how much of your area will get it. When you're told that you have a 50% chance of precipitation today, it means that there's a 50% chance that you will get measurable rainfall (at least 0.01") or measurable solid precipitation (at least 0.1") during the day. Furthermore, it only refers to you at a point, not your entire area.
2.) When you're looking at the models, you look for lots of moisture (high dewpoints and a good flow at 850 hPa bring moisture from somewhere like the Gulf of Mexico), wind shear (winds changing with direction and speed as you go up), CAPE as you said, and boundaries (fronts, drylines, sea breezes, etc.). Using observed data like soundings, hodographs, surface data, radar, and satellite is a better choice over the models if you want to really gauge severe weather potential. The models can't handle convection well enough yet, but they can help you see when a certain setup favorable for severe weather may happen.
Hope this helps!