HI Caoer,
I don't have an EW+, only EW with my own hotrodding, but I might be able to help.
1) Distance should be somewhat larger. Sounds like an internal calibration problem, not front panel. Should be instructions in the documentation; it's a matter of adjusting one high-frequency inductor inside the box. Easy to do, but mark your starting point on the coil in case you get lost.
2) 50Hz: Check the earthing. EW Theremin power supply units in Europe are a problem; some years ago, I ordered a spare from the then German distributor of Moog stuff, and received something that was nothing like the photo on the website. The voltage and connector were correct, but it had no earth connection. A theremin needs an earth connection. So you may need to make some kind of makeshift - an alligator clip to the earth point on the wall or power board socket, and a wire from this to the earth (sleeve) of the audio out plug. This may fix your hum problem as well.
3) The whine on touching the volume antenna seems to be a characteristic of the EW series. Some are ok, many have this issue. Mine has it. My workaround was to wrap a few turns of insulating tape around a portion of the antenna - about 10cm near the front connector to the main body. This gives me a spot where I can 'touch' the antenna (volume 0) but without the whine.
Hope this helps. Happy touchless playing!
Jim F.
PS The then German distributor of the power supply wasn't very helpful when I posed the question at the time. The response I received was 'That's how they are, take it or leave it.' At the recent Theremin Academy Lippstadt, I saw a few people with a workaround similar to my suggestion.
PPS Re Lippstadt: you might like to look at
https://youtu.be/Aw11FMeJo08