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I understand from one of your previous posts that English is not your native language. Thus, we have to work harder to determine what you are saying, and this not a criticism.
In considering the GFCI at this time ignore any question about the AFCI.
I believe you are saying that the GFCI is wired correctly, and when you plug in an external tester that the GFCI does not trip. This is why I suggested an external test resistor back to something that should go to the main panel neutral.
An external GFCI tester such as you probably have will most likely use the outlet ground pin as a path for the test current. If this pin does not have a good path back to the main panel neutral, then you may not produce an adequate test current.
I have not looked back at all of the posts. If you push the TEST button does the GFCI trip? And following this can you RESET the GFCI?
If the TEST button causes a trip and after this you can RESET, then probably the GFCI is working.
After proving that the internal test works, then if the external tester does not cause a trip, check that the outlet ground pin actually has a good current path back to the main panel ground bus and from there to the neutral bus.
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