Personally, I don't have this problem. I always select manual mode and change the speed myself. I never use automatic mode and it shouldn't change all by itself in my opinion.
It is virtually noise free. I use it in virtual calls all the time and no noise perceived by neither myself nor the people I am meeting with. I have it on a old wooden floor.
S1 is the newer version and therefore slightly more expensive. It is slightly lighter and thinner and has a more modern design. Both are foldable and do not have a handle.
The speed is the same for both.
The basic difference is that the motor on the S1 has been slightly improved and, unlike the C2, an app is available in addition to remote control.
I have the Walkingpad S, and it has 2 buttons on the device, M and A as a touch. I managed to hold down the M button on the device and the middle button (Start/Stop) on the remote control at the same time. Then came options, with up, down came speed and there I could unlock the 6. I can't register the apps either, but that's how it works now. Some models have the button on the right side, but that should also work. Good luck and good walk!