Is it permissible to perform ablution in the morning and wipe over the socks for the rest of the day, even if one has not prayed after the first ablution? And what is the permissible thickness of the sock for wiping over it?

There is no objection to performing ablution (Wudu') and then putting on socks (khuffayn). It is not a condition to pray with that purification at that time. It is permissible to wipe over them for a resident for one day and one night, and for a traveler for three days and nights. It is a condition for the socks that they be thick enough so that the skin is not visible underneath them, and that they cover what must be washed of the foot during ablution.