Bathroom remodel electric questions

I am remodeling my bathroom, and as I began to tackle the electric work, I discovered a couple things that were concerning:

1. The circuit that the bathroom (as well as adjacent bedroom and hallway) are on is controlled by a 20 amp breaker. It's actually 2 20amp single pole breakers in the same spot.
2. The wiring that was in the bathroom, that I have since removed all the way back to where the wiring comes into the bathroom, was a mix of 12/2 and 14/2 wire. The wiring that comes into the room, and is the source of the electric for the room appears to be 14/2 (it's old wire with no ground wire and no labeling on sheath, but my wire strippers suggest it's 14/2).

Now I know you are supposed to use 12/2 on a 20 amp circuit, but I don't know the extent of what's on this circuit and what size wire is used throughout the length of this circuit. What should I do to remedy this? I still need to power the bathroom (a vent fan, vanity lights, GFCI). Can I simply switch the 20 amp breaker for 15amps at the box and then run 14/2 throughout rest of bathroom?

It sounds like you have or had knob and tube wiring that might have been converted,
which consists on a Hot and a Neutral With no Ground (which is needed for GFCI, but

sometimes use the Neutral pigtail to mickey mouse false ground,).

*You can add a ground with a wire to copper pipe from sink’s water supply or run to basement)

14-2 wire is rated at 15 amps MAX

12-2 wire is rated 20 amps MAX

If you splice or run off a 14 Gauge to a 12 Gauge you must treat it as a 14 gauge

The higher the gauge the smaller the wire weakest link being 14 while using 14 to 12

If you are rewiring the whole bath and rooms then 12 gauge is the sanest answer

12 Gauge handles 15 or 20 amperes 14 should not be more than 15 for safety reasons

(When using 12 on 20A breaker use screw terminal as opposed to tension insert)

Testing for a hot wire when there is no labeling on wire casing (sheath) use a meter on ~ AC

And use a ground from ground cold water pipe and then touch pos lead on each wire (they do sell polarity test tools also don’t always work with conversion wiring)

The 110 – 120V reading wire is the hot