SX1272 - LoRa - What is the minimal schematic (needed capacitors/resistors) to use that device?
I would call that the schematic from the mBed shield minimal for the most part.
For reference:


You won't want to leave the decoupling capacitors out on the voltage rails.  As for the various inductors and capacitors on the RF antenna line, I would leave those.  Don't mess with that stuff unless you know exactly what you're doing.  I don't do RF design so I can't advise on this.


  Do I need to somehow calculate them by myself? How to do it? 


The values of the components in the RF antenna path, those are very tailored to the PCB design and antenna design, it is very specialized work.  If you want to make a watered down version of the mbed shield, you can just use what the values are in the bill of materials, which is in that same zip file that contains the design files for the mbed shield, so long as you also use the same PCB design for the antenna.


  As I understand, the SX1272 can not be programmed? - Ie. Upload your
  own program?


Right. The SX1272 is merely a modem/tranciever IC.  There is limited configuration of the GPIO pins which can be tied to do certain actions but you won't be programming it in any manner similar to an atmega.