What happens if a character wins the test? Does he/she move normally on the path, or does he have to win a mental duel each time he/she enters a circle on the path that Heizinger controls? Because it says that "A given character may only initiate this Mental duel once per activation", and then it also says that "This duel must be fought each time a character wishes to enter into a circle on your path".

Also, what happens if the character loses the duel, but he/she is in the middle of an isolated path and he wants to move inside the path, or he/she is on a circle belonging to two different paths, that are both controlled by Heizinger (this happened to me in the central area of the Catacombs, with a Commando Delta being on a red-pink circle, and Heizinger being on another red-pink circle, and the Commando wanting to move on another red circle and losing the duel)? Does he/she have to duel for entering the second path which is also controlled by Heizinger, or does he/she move normally, or he/she is not allowed to initiate another duel, therefore unable to move onto the other path?

This question has been reviewed many times on this forum. FFG have failed to provide a definitve answer. I use just one test and if you pass then you are free to move on the path. Others only allow one step as you can only take the test once. If you are in the middle of the path and fail, then you are stuck.

Search the forum for more details.

I already checked the forum, but the answers are at best ambiguous, leaving the players to interpret them as they want. The text of the entire rule is being either taken ad literam or not. And regarding the actual game play, the Hermetica is either OP or slightly useless.

You have nailed the problem. The answers are ambiguous. Hopefully it will clarified.

I do use one attempt and allow the model to continue without interference if they pass, otherwise they cannot move in the path.

Yeah, probably best to use it like this.