CiA 402 Folder Missing

Yes, I can jog the axis and tried simple MDI commands that work fine.

Congratulations
I don't think the rest should be a problem

Thank you, but I have not executed any homing procedure. I thought that I should execute a homing procedure at least once. For example, let us assume that I utilize the index pulse homing method - 34. I execute homing once and then the servos have their reference from the absolute encoders.

You have not Stepper online A6 servos

I achieved some kind of success in homing the servo motors using the CiA402 home component. There is still a problem when the homing is executed in a certain situation. Basically, I am using homing method 34. Then using the halshow I set  the 'request-custom-homing' pin, the homing procedure starts but when the servo find its Z pulse it start moving quite fast. Perhaps it tries to reach a certain position but LinuxCNC reports 'joint 0 amplifier fault' and the servo drive error is 'Position deviation is too large'. You can see videos of what is happening - one video in normal velocity and one in slow motion.  Videos
This behavior of the drives can be observed the the actual position is above 35 000 000 pulses. When the homing is started below this pulse number, the motor finds it Z pulse and the move quite fast to the position where the homing was started.
Attached are the configuration files.

Did you connect the origin switch to the servo?
It's usually called the HOME switch.
The VECON manual is really terrible.
It doesn't say anywhere where to connect the limit switches and the origin (home) switch.

Method 34 is using only the Z pulse of the encoder, no homing sensor is needed for this homing method.
The homing sensor is connected to any of the digitals input pins of the drive. It is not assigned by default, i. e. it is configurable.
I just tested homing using a homing sensor with homing method 19. But still, the drive behaves the same way as in the video - starts looking for the sensor at high velocity, when rising edge is triggerred the motors reverse at slow velocity, when falling edge is triggered the motor starts moving quite fast and position deviation errkr is triggered.