My turn to add some stuff. In the US it is permissible to replace an outlet with a GFCI and no ground if labeled as such.
#2. The 1/2 the line voltage happens when there are filters on a circuit, and they are usually symmetrical, so they feed back about 1/2 the line voltage to the ground pin if open. I totally understand where the phantom voltage comes from and why it's usually about 1/2 the mains.
So, in the gist of things, it looks as if you have an open ground. I just troubleshoot one of these problem, but it isn't totally fixed yet.
If it's a metal box, then the device and the box both have to be bonded. You are not allowed to relay on just the screw.
You might trip the GFCI's and see if the bedroom circuit dies.
Although, I haven't had to do this, but what I would do is either use a voltage detector probe or use a circuit breaker locating device, to trace the feed to the outlet with a broken ground.
So, you kinda have to know which outlets are on that circuit and then guess where the wires go. In one of the boxes, the grounds may be just twisted and not wirenutted together. The oxidation breaks the ground even though they "LOOK CONNECTED".
There are some devices and techniques that are helpful. Older boxes do not have a tapped ground screw hole and that makes things difficult. You have to use clips and solid wire. There is a lot of ground stuff here:
https://en.wikipedia.org/wiki/E_(mathematical_constant) that's helpful. See this catalog under grounding: **broken link removed**
I can't seem to find a product I use which is a wirenut with a wire coming out of the other end. The solid and stranded pigtails are available in a hardware store.
So, anyway when you find a break in the ground, now you have to guess which outlet feeds the bad one. Yous should be able to trace the wire in the wall with a breaker tracer or AC voltage detector. So, it could feed something downstream or be fed from something upstream. You can disconnect the hot at the bad outlet and you should then be chasing the feeder wire.
Connections can look good, but be bad if they were not done right.
In my case, the ground actually was made from a 50' piece of coax to the coax ground block in the attic. The local ground was missing. So, this outlet was grounded with 16 ohms resistance. The antenna amp has a 3 prong plug and guess what circuit it was plugged into?
So, you may have to (with the power off) measure the resistance of the two touching ground wires with sharp probes.