And finally, if an UPS is used, doesn't the server applications need to have support for it? outherwise the power outage is only delayed? Or is it only the operating system that needs the UPS? Why is an UPS needed for a server but not for clients?
Who says that clients don't need a UPS? All systems in our environment are protected by a UPS - from every server to each desktop.
You are correct that a UPS only delays the power outage. However when a power loss occurs the UPS communicates to the OS through a USB cable (most common nowadays). This allows the UPS to notify the OS when the battery is about be empty and the OS can begin gracefull system shutdown. This is something that is not possible in a normal power outage without a UPS. The power company will not call you and tell you that a tree is going to fall in 10 minutes and kill your power.
Your assumptions about how a computer handles a loss of power are not realistic. Most of the time there might not be any harm, but there is no need to gamble. One problem on a production server and you will rue the day that you decieded you did not need a UPS.