Is it a condition for wiping over the khuffayn (leather socks) to wear them immediately after purification, or is it permissible to wipe over them even if there has been a long interval, provided wudu' remains, and is intention a condition for wiping?

It is not a condition for wiping over the khuffayn (leather socks) to wear them immediately after performing taharah (purification). Rather, the condition is to wear them while in a state of complete taharah. So, if one wears them a long time after performing taharah, and the taharah is still valid, there is no harm in wiping over them.