I just bought a couple of bikes and I noticed that the little screws that hold the brakes in place are NOT screwed in all the way. Should I screw them in until they are tight OR do they need to be screwed in only half way?
No, they are there to adjust the spring tension on the brake arm. You turn them in to provide more spring tension and out to lessen it. You want to balance them so the brakes release evenly. That way the brake pads can be very close to the wheel without touching it. On caliper brakes used on road bikes it centers the brake calipers.