Traveltech:
I'm not really sure what information you are questioning, or what information you don't understand.
I explained quite clearly how the Nf governor will function in the forward thrust range of propeller operation, thus your statement ...as I understood, the Nf governor is only active in the beta/reverse range... is not correct. The last two sentences in your post are confusing, it is not clear if you are making a statement or asking a question.
Best suggestion I can give (and please appreciate that I am NOT trying to be sarcastic here) is that you print out this thread, then review the discussion and explanations carefully on the printed pages. It is often very difficult to follow the something like this just by looking at it on the computer screen. If you then want to make any specific follow-up questions about points you don't understand, or think are not correct, post specific questions or a specific hypothesis.