Headaches are only rarely caused by eye problems, even if the pain feels like it is coming from or behind the eye. One explanation for this perhaps surprising statement is that the eye socket is often the site of "referred pain", that is, a sense of discomfort in one part of the body because of a problem that is truly elsewhere. This is similar to the occurrence of left arm pain in patients who experience a heart attack. The need for glasses is not commonly an explanation for headache, although you might feel "eye strain" or tire more easily if a better prescription for glasses is needed. Headache should be distinguished from true eye pain, which is usually localized to the surface of the eye, and is most commonly caused by dry eyes.
Visual loss occurs because of either optical or neural problems. Optical causes of visual loss [such as refractive error (need for glasses), cataract or corneal opacities] can usually be corrected or at least significantly improved. Nerve damage (for instance to the retina or optic nerve) cannot be repaired. Researchers around the world, however, are working on many strategies to restore vision to patients who have suffered damage to the retina or optic nerve. To date none of the laboratory techniques have been successful in this quest.
Yes, definitely you should be examined by an ophthalmologist as soon as possible. Temporary loss of vision that persists for at least several minutes can be a sign of interruption of blood flow to the eye. Temporary visual loss can be followed by visual loss that is permanent. By analogy, a few minutes of chest pain can be a sign of an impending heart attack, and the importance of contacting your doctor in this situation seems obvious. The same concern should be given to visual loss that persists for several minutes or longer, even if visual loss is confined to one eye. Not all causes of temporary visual loss are serious. In fact, migraine is the leading cause of temporary visual loss (even when not accompanied by headache) and vision almost always returns to normal with migraine.
No. You should wear whatever prescription is determined to be correct for your eyes. You will not harm your eyes if you do not wear your glasses, and you will also not harm yourself if you do use your glasses. The notion that wearing glasses weakens your eyes derives from the common observation that people who begin to use reading glasses typically need to increase the strength of the prescription after a period of a few years. This need for added strength results from a naturally occurring age-related change in the lens of the eye. It is natural to need stronger reading glasses at age 60 compared to age 40.
No. Exercising muscles of the eye improve neither their ability to focus nor to move from side to side. This might seem counterintuitive since all other muscles of the body can be made to improve their performance by exercise, but the muscles of the eye are different in this regard. The difference might partly result from the fact that the brain provides very precise control for eye position and exercising the muscles does not influence the signals coming from the eye to the brain.