Firstly, Singapore - Perth is now 2-class configuration using the SR* series of aircraft on all flights. Only one of these aircraft is fitted with the new Matsushia 3000 WISEMEN system in both classes. In September, however, I did travel aboard a 3-class aircraft but the general rule is 2-class.
As for finding out whether your aircraft has Skysuites or not, the best place to check is singaporeair.com and check the schedules. Click on the aircraft type and it will show you the seating configuration for that particular flight. The only exception is the 777-ER which for some reason hasn't yet got a seat plan and therefore shows a 3-class 777 layout. Johannesburg is still using the old seats as a rule but SIA recently decided to upgrade Auckland to the Skysuites so perhaps they will do the same with the African routes.