A good approach makes for good landings. Steady airspeed, steady descent rate, small corrections. As you see the runway start to grow in your peripherals, remove the power and start to flatten out, bleeding off any excess airspeed prior to touchdown.
As for the centerline, it sounds like you are very critical of yourself, thats good and bad.
A good fix for the centerline problem, pay your instructor an extra $5 for every miss, you will get much more accurate, quickly.