What is the ruling on the clear, viscous fluid that exits after urination, is it considered impure, and how should one deal with it in terms of ritual purity (tahara) and repeating ablution (wudu)? Also, is wiping over shoes instead of washing the feet permissible in ablution when praying at work, given the absence of a designated prayer area and the necessity of sitting during prostration?

The fluid discharged after urination is "wady," which is impure (najis). One must purify themselves from it and perform ablution (wudu'). It is advisable to use tissues or similar items to prevent the impurity from spreading. Once it stops, you perform ablution and pray. As for prayer (salat), it must be performed with its actions, including standing, bowing, and prostrating, in their proper manner. If a suitable place is not available in the room, then prayer must be performed in another location, and the pillars of prayer must be performed in the prescribed manner as long as the worshipper is able to do so.