How/Why did Tyler Durden got shot in the head?

From the movie Fight Club, in the ending scene we can see the narrator shoot himself in the mouth asking Tyler to "really listen to him"...

The question is How/Why did Tyler got shot in the head when the narrator himself shot in the mouth? It could have been somewhere else and not the head, right?

Is this just because the Narrator "really" wanted Tyler to listen to him and die?

Since Tyler is just a hallucination, we know that Tyler dies when narrator mind accepts his death. The narrator can't do this on his own, since he needs Tyler's permission to do so (otherwise why would he ask Tyler to listen to him?). Now, if he really wanted Tyler to die, he could have shot Tyler directly and imagined his death, which would have lead to the end of Tyler.

Is this shooting scene in the significance of "Fight Club" where the narrator wanted to shoot himself just with the spirit of hurting himself? Does this indicate that Narrator and Tyler became one at the end?

Was that shot really needed to kill Tyler? What would have happened if Tyler also got shot in his mouth and was alive instead of getting shot in his head?

I have attempted the plot-explanation, but I watched the movie only once long back... I would be glad if someone can expand this/ explain this even better.