Wiping Over Socks and Casts

• Is prayer valid after wiping over a second sock, worn while in a state of purity after removing a first sock that had been wiped over, given that ablution was not nullified between the two wipings?
• Does one have to repeat the prayers of the second and third days if a person prayed while wiping over his socks for three consecutive days, knowing that the duration for wiping for a resident is one day and one night?
• Is negligence in ablution—such as not completing it, or forgetting a part of it, or wiping over socks due to cold—among the justifications for not completing it? And will Allah punish one who negligently fails to complete ablution out of forgetfulness?
• What is the ruling on the prayer of one who wipes over their socks, either by having their wife wipe for them, or by using a wet broom, or by spraying water on the top of the sock with a sprayer? And is it legislated to pour or spray water on the sock or Khuff (leather slipper) whether out of necessity or not?