The lounge is open 24hrs.
http://www.changiairport.com/in-transit/airline-lounges
UA operates from T3, the *Gold lounge is the Krisflyer Gold lounge.
As mentioned above, you are in the airside part of the terminal as soon as you get off the aircraft, so no need to do anything other than go straight to the lounge or transit hotel and then to your gate afterwards.