Understanding the second transformer in PoE designs
T3 is used to check the maximum current flowing into the mosfet drivers - it's a current limiting device. If you look in the normal data sheet it replaces the component below: -




  Can I combine both designs, use a current sensing resistor on the
  primary side and a perfect diode on the secondary, and leave out the
  second transformer completely?


There's no connection between current monitoring on the primary (via T2, a current transformer) and secondary side rectification.


  Is this really proportional to the current on the primary side of the
  main transformer?


It's a 1:100 CT so it's going to work fine even though the burden (R12 @ 11 ohms) is after the rectifer D9.