I want to ask about wiping over the socks. If I take off my socks and then my ablution is invalidated, and I wear them again after a while, so when I want to perform ablution again, can I wipe over them, or I am obliged to wash my feet and then wipe over them the next time I perform ablution?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The last option which you mentioned is the correct one, as it is a condition to be in a state of purity in order to wipe over the leather socks and the like, like light cloth socks, because if someone wears them when he is in a state of minor or major impurity, he cannot wipe over them. The evidence about this is the saying of the Prophet : "Leave them (the socks) as I wore them when in a state of purity." [Al-Bukhari and Muslim] The Prophet said so when Mugheerah Ibn Shu’bah wanted to remove the socks of the Prophet as he was pouring water for him when he was performing ablution. 

Allaah Knows best.