In ,
Charlie Bress wrote:

A quick test is to turn off the breaker protecting that branch and
see if reset works.

On all GFI's I've worked with, the test and reset buttons are both
inoperative in the absence of power. The reset button will not "click in."

The GFI tester is telling you the truth. The voltage detector is
giving you a false positive.

Yes, the GFI is telling the truth. The OP has problem with the neutral
wi
"I get hot reading when I test either side of the outlet."

Shouldn't get a "hot" reading on a wire (the neutral) that is tied to ground
at the panel.
--
Jim
"Remember, an amateur built the Ark; professionals built the Titanic."