Taking your errors into consideration it indeed looks like you are a fine candidate for a Laser Vision Correction surgery. Just as your doctor said, the thickness of your cornea (along with few other parameters) has to be checked to fully qualify you for a surgery. It is not uncommon for the pupils to be decentred but to determine whether the misalignment of your pupils will be an obstacle during the surgery I would have to examine them. Usually the cornea heals for about 10 days and after that you can return to physical activities. However I would strongly recommend you to avoid strenuous exercises for at least a month after the surgery. The mentioned complications are extremely rare (according to multiple studies the probability of all of complications is lower than 0.5%). It is hard to tell what causes them as the main purpose of the qualification process is to rule out any risk of them occurring. Despite that, after Laser Vision Correction, just after as any other surgery, some complications may occur.