Bad accuracy with my cnc machine

[JAZZCNC]

How do i check if pulse signal is set wrong in drive?

Depending on your drive it will have either a switch to change the Active edge or software setting. If not then it will be fixed and the documentation should state the rising or falling edge.

Yes there is some noise while running in air, some strange noise like clicking. Starting point is not the same, its like 3-4 mm deeper when the program finished.

I don't mean noise has in sound.! . . . I mean Electrical interference noise EMF from other components around like Spindles etc. Looking at the condition of your wiring with motor wires unshielded and probably poorly grounded control box then it's a Huge chance this is your problem.!

What does active edge means, what is it used for?

This means the point when the drive issues the Step signal. It can be the rising or the falling edge of the signal Pulse. (also some controllers look for the Step on certain edge.)
If your drive issues the Step pulse on the falling edge of the pulse and your controller is expecting seeing it on the rising edge you'll have timing issues. Often when active edge is wrong you'll loose 1 step or micro step for every direction change.

One common mistake made is that people will wire the motor phases wrong. ie: Put A+ to A- on the drive connection. Then when the motor spins in wrong direction they just change the Active hi-low state in Mach motor outputs and it spins in correct direction.!! . . . BUT this now means the control (mach3) is looking for the Step pulse on a different edge and if this edge is the opposite edge to drive then you could have timing issues resulting in loosing position.
The correct way to change an axis direction if needed is using the Reverse option in Home and Limits.

If you wire the motor phases correctly to the drive. ie: A+ on motor to A+ on drive then 99% of time the motors will spin in correct direction and will match the Active edge set in the drive. This is often the rising edge but some drives like the Geckos do use the falling edge in which case if the motor phases are set correct then you would set the Active step edge in motor tuning to match. ie Step low active ticked.

Another common cause of positional lose with parallel port revolves around timing issues and the Kernal speed set in Mach3.?
The pulses created only have a certain time interval between changing state and the higher you have the Kernal speed the shorter interval. So if you set the Kernal speed high you shorten this time interval so combined with high motor tunign it's very easy to lose Steps. This is why it's recommended with parallel port to keep Kernal speed set at 25Khz for most stable performance. Every change up in Kernal speed increases chance of unstable system.