Electronic – Role of zener diodes accompanying High power UV Diodes

The diodes are there so that there can be two separate mechanisms for enabling the main headlight relay without interfering with each other. From the labels on the right, it looks like the two mechanisms are the normal headlight switch, and the momentary passing switch, which makes sense. You want each to be able to turn on the headlights independently.

Added:

You now say you are looking for more of a low level electrical explanation of what the diodes do instead of the high level conceptual explanation you originally asked for.

The diodes allow either switch to turn on the relay, but still remain independent. Presumably at least one of the switch lines is used elsewhere in a way that it shouldn't be signalled when the other switch is activated. Without the diodes, there would be only a single switch line, and that would be activated identically by either switch, making it impossible for other parts of the system to determine which user action caused the headlights to turn on.

For example, the general headlight switch may also turn on some running lights or maybe a indicator on the dash that the passing switch is not supposed to turn on. With the diodes in there, the general headlight switch line remains unasserted when the passing switch is activated. Each switch can activate the relay, but there is no connected between the switches.

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.