"1)When it rains is it true you get worse gas mileage? If so, why?"
I would say Yes, your mile per gallon would decrease because there is slightly more resistance on all four tires. However, I don't think the rain has a substantial effect on MPG, unless that is your driving in a 1" puddle of rain.
"3)How does humidity affect engine power output (and gas mileage)?"
Humidity means that there is a tiny water molecules in the air. When driving in humidity, air, along with vapors, is drawn into the cylinders.
Water is denser than oxygen which means that there is less potential to make power because there is slightly less oxygen and the water has taken up more of the "space" in the cylinders.
Hope that makes sence, or correct in that matter!