Most lasik surgery are done on both eyes at the same time to avoid the problems caused by unequal vision. If your both eyes are nearsighted and you only have lasik surgery in one eye, you still have to wear glasses.
It depends on your personal preference. Some people would have surgery on each eye separately because because they don't want any possible complications to affect both eyes which they would be unable to see with neither of the eyes.
Of course you can. It just depends on your preference. Most people will choose to have lasik surgery on both eyes at the same time so that they can get good vision for both eyes. While some people would like to have each eye done separately because they just want to avoid the side effects affecting both eyes.