Yes, you can paint over wallpaper if it is firmly stuck to the wall, in good condition, with no peeling edges, bubbles, or moisture damage. Clean it, repair the seams, seal it with an oil-based or shellac primer, then paint two coats.
To repair drywall, fill small holes with spackle, cover medium holes (up to 6 inches) with a self-adhesive mesh patch plus joint compound, and cut a proper drywall patch with backing boards for large holes.
Wall studs are the vertical wood or metal framing members behind your drywall, usually spaced 16 inches apart. The fastest way to find one is an electronic stud finder: calibrate it on a stud-free section, then slide it slowly until it signals.
