All you need to do is turn the screws on the bridge posts clockwise to lower the action. I'd suggest you de-tune the strings a bit to reduce the tension on them, and try turning the screws a half-turn at a time. Re-tune, and see if you're happy; if not, repeat the process until you have the action where you want it (without buzz, of course).
As for pickup heights, usually the neck is a little lower, as the strings vibrate more at that point than they do over the bridge (so "louder"). If the heights are exactly the same, you'd usually find the neck output volume to be louder than the bridge, and most folks want them to be about equal. But it's all about what *you* like - both pickups are totally adjustable, and moving them closer to/farther from the strings will also affect their tone. Experiment with both, see what you like. There are no rules! The four screws in the corners of the pickup rings keep it mounted to the body, so the two screws in the middle of the short sides are what you use to adjust height. Turn clockwise to lower, counter-clockwise to raise. A little goes a long way in changing the tone/output, so small adjustments, play and see how it sounds
