Yes. There are four types of refractive error which may occur singly or in combination: hyperopia (cannot see close), myopia (cannot see far), astigmatism (blurring at all ranges), presbyopia (inability to focus). Each of these are tested for by your ophthalmologist and glasses may be prescribed to optimize vision.
Yes. Glasses can correct myopia/hyperopia and regular astigmatism (low order common abberations) but there is also irregular astigmatism that can be corrected with rigid contact lens. Plus wavefront can now detect higher order aberrations.
Sort of. You can have myopia (near sightedness) and astigmatism and hyperopia (far sightedness) and astigmatism, but you can't have both myopia and hyperopia.