Can eye exercises prevent or correct refractive errors?

Not really. Refractive errors are intrinsic to the eye structure and are best corrected with glasses, contact lenses or lasik. In some cases of early presbyopia or difficulty reading, reading glasses may be delayed a bit with accommodation exercises but inevitably patients will require reading glasses.
No. But sometimes a myopic shift can happen with time (the refractive power of the eye changes), and thus a hyperopic refractive error can be reduced. Eye exercises might reduced eye strain, i.e. Convergence insufficiency.
No. This in an area of a lot of contraversy in ophthalmology. There are a few drs that charge pts a lot of money for "vision therapy" that they claim will reduce glasses dependency. It has been proven time and time again that with the exception of pencil pushups for addomodative insuficiency there is no benefit of eye exercises what so ever.
Reading=worse. Reading may actually cause nearsightedness to increase. Recent studies show an increase in myopia in patients who spend a lot of time with near activities. So that form of exercise may actually make refractive error worse.