Having only 10-15 pounds of pressure in the tires would make the handling really, really sketchy for sure. Also check to make sure that any quick releases on the axles are properly tightened because if they aren't, things get interesting in a hurry as well.
As for sizing, the bike's probably not too big for you if you can straddle the top tube with both feet flat on the ground.
For adjusting seat height, I usually start with the seat set up so that my leg is fully extended at the bottom of the pedal stroke with my heel on the pedal. No, you don't ride with your heel on the pedal, but this tends to give the knee about the proper amount of bend when you ride with the ball of your foot on the middle of the pedal. Note that if your seat height is properly adjusted for efficient pedaling, you will probably not be able to put both feet on the ground at once while sitting in the seat, unless your bike is a cruiser or similar geometry.