SMPS coupled inductor selection
Why is it driven with rectified mains which equals to 375 VDC?


It isn't, the rectified mains is alternately switched onto the primary of the flyback transformer (in order to store energy) then it is disconnected thus allowing most of that stored energy to be transferred to the secondary winding. U1 does that switching: -




  the duty cycle does in fact, like in a buck or boost converter, affect
  the ouput voltage?


Correct.