Is it permissible to wipe over the head and the khuffayn with a dry hand? And what is the sufficient amount for wiping over the khuffayn and its conditions, along with the proofs?

The obligatory wiping for the khuff (leather socks) is to wipe their top, not their bottom, based on what Abu Dawud and others narrated from Ali (may Allah be pleased with him) that he said: "If the religion were based on opinion, then the bottom of the khuff would be more deserving of wiping than its top. I have seen the Messenger of Allah (peace be upon him) wiping over the top of his khuff." Scholars differed regarding the sufficient amount for wiping the khuff. The Shafi'i school holds that it is recommended to wipe its bottom, and that the obligation is to wipe the smallest part of its top. Others held that wiping the bottom is not recommended. Abu Hanifa held that it is obligatory to wipe an area equivalent to three fingers. Ahmad held that most of its top should be wiped. Malik held that all of it should be wiped except for the creases. The safer approach is to wipe all of it to avoid dispute. The hand must be wet when wiping.