Do frequent movements—such as raising one's hand to adjust clothing or looking at the wrist to ensure it is not exposed—invalidate the prayer, and does it invalidate the prayer in the case of adjusting a bothersome hijab, and what is the ruling on forgetting that these movements occurred during prayer?

A Muslim must approach his Lord in prayer with humility and devotion. Excessive movements in prayer invalidate it, whether done intentionally or out of forgetfulness. Much movement is that which makes an observer think that the person performing it is not praying. As for few movements, there is no harm in them, such as adjusting a headscarf if it can be done with few movements that are not considered excessive by custom.