/diy/ - Do It Yourself

How does electricity work?
I recently had a well issue, so I learned a bit about well pressure switches and had to replace mine.
First to troubleshoot, and then for safety before replacing, I used a multimeter on my pressure switch when the contacts were open.
I don't know correct terms so I am going to say 'input' to refer to the wires carrying electricity from my circuit breaker to my pressure switch, and 'output' to refer to the wires carrying electricity from my pressure switch to my well pump, sorry if that's the wrong words.
Touching one of my multimeter leads to the input hot wire and the other to the input neutral wire gave me a reading of 220V. Touching one of my multimeter leads to the input hot wire, and the other to either ground or an output wire gave me 110V (when the pressure switch contacts were open, meaning no electricity was flowing through the output wires). Touching one of the leads to the input neutral and the other to ground or output also gave me 110V.
However, it is my understanding that only the hot wire carries electricity from the source (breaker) to the destination (pressure switch or well pump).
So why is it that neutral to ground or neutral to disconnected output was also giving me 110V?
Is this because there was electricity flowing through my breaker box due to my other breakers for my other appliances or what?
What is the neutral wire doing?
Also, my pressure switch has two ground wires, one coming from the input wires and attached to the metal body of the pressure switch, and the other coming from the output wires and attached to the metal body of the pressure switch. Both are connected to the same metal body. Obviously I am going to leave them both attached, but purely theoretically, they serve the same purpose, so I would really only need one or the other of the two ground wires connected, so I could disconnect either one and still be completely safe (assuming there's no broken wire anywhere, etc), correct?

My well pressure switch is often not going on when it is supposed to, meaning my water goes out and I have to flip my pressure switch reset lever. Multiple times a day.
Can this be caused by too low air pressure in the pressure tank, and what other causes can happen?
Background:
>few weeks ago, water goes out, which ultimately was due to a frozen pipe, but while troubleshooting I replaced the pressure switch with a new identical one (20-40)
>after getting the pipe unfrozen and everything working, that first day my water went out while showering 2-3 times so I had to reset my pressure switch each time
>after that, it was completely fine with no issues for a week or two
>at some point, don't remember exactly when, I let a few psi of air out of the pressure tank because it was slightly over 20 when in fact it should be slightly under 20 since I have a 20-40 switch
>now as of a few days ago, it has started going out frequently again, so each time I have to flip the reset lever
>I tried raising the cuton/cutoff pressure on my switch by tightening the big spring, that didn't help
What is likely the cause of this? Should I try raising the switch's cuton/cutoff pressure more, or lowering the cuton/cutoff pressure, or raising or lowering the air pressure in my tank?
The issue is all right at the pressure tank and/or pressure switch. It is not the breaker or anything else, breaker is not tripping, only the pessure switch is tripping.
Thanks