I recently quit smoking and I have already notice an improvement. How long does it take lungs to repair?

Depends. On how long and how heavy you were smoking, as well as individual susceptibility to damage, which varies considerably. Some people smoke heavily and do relatively little damage, others smoke much less and get a great deal of damage. In general, the lungs clean themselves out in 3 months or so.
Varies. When one stops smoking, one is able to get out the junk that has been accumulating in the lungs over time, and lung function improves. Any destruction done to lung tissue (e.g. Emphysema), however, is permanent. After stopping smoking, the lungs deteriorate at a normal rate rather than the accelerated rate of active smokers, so you have done yourself a big favor by stopping smoking.