Bathroom and left bedroom outlets don't work and light in kitchen won't work. The outlets in the kitchen work though. Breaker isant tripped. Gfci outlet test button won't reset. How do you test the wiring on the back of the gfci to see if power is even going to it?
Checked each breaker with neon tester to see if power is there. All have power going and coming, but I think there might be a break in the line case the gfci won't reset.
A few days Before the outlets stopped working the lights were all flickering. When the bathroom light would get turned on, the fan plugged in the bedroom went faster, not slower like if power was being drained.
Also two of the breakers are double-tapped

If the GFI breaker will not test or reset, obviously it is defective.

I am confused, di you or did you not test the line side of the breaker?

There should be power on the main bus serving the breaker.

FPE Stab-Loks can be tricky whe they plug into the main bus, could be some corrsion or melted metal on the stabs, causing an open circuit.

May need to relocate breaker to an unused slot.

Be careful working on an open energized panel, be sure to be wearing voltage rated gloves and fire rated face shield or safety glasses.

The Federal Pacific Stab-Lok panels are potential hazards... do an internet search to read more...
Replacing this panel would be a good idea as it's likely already 50 years old and may solve some of your issues.