How will radiation therapy for a brain tumor change my facial skin?

None: The treatment is aimed rather precisely toward the tumor and radiation doctors should not allow it to go through your face. The scalp however is different. You will likely lose hair unless the tumor is very small and special techniques like cyberknife are used. If your whole scalp or large areas are treated then hair will most likely temporarily fall and the skin there might get red then heal.

Not much: Radiation effects the organs in its field including skin of the scalp(dryness) and hair (hair loss). It should not effect the skin of the face unless it is near the brain radiation field.

Varies: It depends on the dose. Acutely it may appear to be slightly tanned or inflamed. These concerns should be brought to the attention of your treating radiation oncologist.

It shouldn't: Beams going through the scalp and directed at the brain should not affect the face. If beams travel through the face then they could but typically the face is spared of energy going through it to reach the brain.