Why to double reverse diodes in parallel to MOSFET?
I understand that reverse diodes inside MOSFET package are put there to protect the transistor from inductive reverse current.


Actually the internal diodes in MOSFETs are a not there explicitly for that purpose. Normally MOSFETs would be a 4-pin device with source, drain, gate and body terminals. But because these are "not that usefull" and the body terminal could cause inconvinience forming a PNP or NPN transistor inside, this gets shorted to the source preventing that. Thus the body diode gets formed.




  Why to double reverse diodes in parallel?


The external diodes are used in this schematic, because the used MOSFETs have a high turn on voltage for their body diodes. N-channel has a body diode voltage of 2.5V and the P-channel has a body diode voltage of -6.3V.  Meaning the voltage would have to rise above 2.5V or below 6.3V for the internal diodes to start conducting. This could be a problem and damage the devices and I guess the designer just want to be completely sure nothing bad happens.




  Maybe external diode can be ignored if the transistor packaging includes the reverse diode?
  Maybe some special diode should be place in addition to MOSFET internal diode?


Usually the internal diodes are sufficent. But if they have a high turn on voltage such as your P-channel and even your N-channel has relatively large turn on voltage, external diodes are placed like in the schematic. If speed is important in your project, I would recommend using schottky diodes as these are much faster than normal, and have a lower turn on voltage.