How long does the Wudu last if one is sure that he has not lost the state of being in Wudu by urinating passing wind etc, etc? Is it permissible to perform Wudu without washing ones feet if one has been wearing shoes and socks since the previous Wudu? Say from Zuhr Wudu to Asr Wudu.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The Wudu remains valid as long as it is not nullified by one of its known nullifies like urine, passing wind, sleeping, … etc. no matter how long this takes.
But if the person is wiping over a sock or a shoe, then his Wudu cannot be valid for more than one daylight and one night (24 hours) if he is not a traveler. If he is a traveler the period is 3 days and their nights.
The evidence for this is the Hadith reported by Muslim from Ali Ibn Abi Taleb that "the Prophet (Sallallahu Alaihi wa Sallam) set a day and a night for the settling person and three days with their nights for the one traveling" .
Imam Ahmad also reported from Awf Ibn Malik that the Prophet (Sallallahu Alaihi wa Sallam) ordered to wipe over the shoes for 3 days and their nights for the traveling person and a day and a night for the non-traveling person. This is the opinion of most scholars of Islam.
Allah knows best.