To answer the first question, a front separates two airmasses, usually warmer and colder. Many things affect temperature, including fronts. As the name implies, a cold front means the cold air is moving forward, and temperatures will drop as it passes. A warm front will cause temperatures to rise.

To answer the second question: Yes, air pressure is related to temperature. Given equal volumes, warm air is lighter (less dense) than cold air and consequently exerts less pressure.

That being said, the relationship with highs and lows is less clear. You can have bitterly cold weather under a strong arctic high, or very hot weather under a warm summer high. With clear skies under a high, you get more of the sun's energy through to the ground to warm things up, but a thin layer of cloud trapped near the surface can limit the warming of the sun.