Function and operation of MOSFET drive circuit with MELF diodes D1, D2, D3 (Vf 0.2V)

Hello everyone,
I have made a schematic (circuit) (attached as jpg) following layout on the PCB board that I found in battery charger device.
Don't know if I have done a good job and is this circuit made correctly.
It looks like a MOSFET drive circuit, but can not understand the function.
I would like to learn and understand function of this circuit.
It would be really great when someone can explain me how does this circuit works and diodes (D1, D2, D3), which type of diodes are they, MELF package, marked with a blue band, Vf = cca. 0,20V.

Thanks in advance.

If the purpose of your project is to just learn about devices, I would start with a more basic circuit, designing with BJT transistors requires some solid analog understanding to make them work correctly in the "analog region" (i.e. not switch on/off).  There are a lot of great tutorials out there and simple kits to help in understanding how devices work.  Some favorites include: Sparkfun, Adafruit, and Qkits(out of Canada).  Good luck.