Will hair grow back on the scar of a cut on the scalp?

Usually not. Scars occur between the follicles and can be of varying widths. If the scar is quite wide, sometimes it makes sense to cut out the scar and bring the scalp together to narrow the new scar so that the gap between the hairs is not as great. Unfortunately, if the scalp is pulled too tightly, tension can kill the hair follicles at the edge of the incision and result in a wide hairless area again.
Not on a cut. A random laceration won't have hair grow through it. A well planned incision, if performed properly, can have hair grow through the scar. Depending on location, the lack of hair is usually not much of an issue. However hair transplantation and/or scar revision may be beneficial if needed. Your local facial plastic surgeon can advise you.
Maybe. It depends on how the scar heals. Sometimes the injury or scar tissue damages the hair follicles and hair may not grow back in that area. This is more true if the scar is widened or thick. Hair growth depends on the follicles, and whether they are damaged. It is possible hair may grow in a different direction.
No notable hair loss. While the scar itself, generally a fine line about 1 mm wide, does not have hair follicles, there should not be any notable hair loss around the scar and it will be completely hidden by the surrounding hair.
No hair in scar. No hair does not generally grow in a scar as the hair follicles do not exist in scar tissue. Scars are sometimes zigzagged (w plasty or broken line scar) in order to avoid the hair "parting" along the scar which can me most visible when your hair gets wet.