Controling switching regulator digitally
What is the purpose of those two schottky diodes? isn't it causing voltage drop which we have to compensate in software?


No, because the current and voltage are being by PI controllers; any offset from the diodes is compensated by their integral action.


  How the opamp in voltage section works, is it comparing OUT+ with OUT- or OUT- as ground because of low-side current measurement?


It is comparing OUT+ with OUT-.  OUT- is probably the actual output terminal of the supply (see where it's connected to R7).


  What's the VCC voltage for the voltage dividers next to the opamps? is it the same as OUT+?


VCC is generated somewhere else; it's almost certainly a clean reference voltage (or should be).  It would not be sensible for it to be OUT+.