Yes. It is possible and many pilots have had laser vision correction. There are many different vision requirements for aviation from civilian, commercial and military. You have to carefully check the requirements that meet your goals.
Possibly. Your ability to become a pilot depends on the requirement set for the position. Most military pilots and commercial airlines do not allow prior lasik. Other opportunities may not have this requirement.
Yes. In fact the us military has done studies on aviators. In some cases prk is ok, in other wavefront all-laser lasik is approved.