You might be interested in these things called mouse jigglers, they range from a tiny USB dongle that simulates a mouse, to motorised movement pads that you can place under a real mouse, which would be undetectable by software.
Just be careful using them at work as there are other methods to detect if someone is working or gaming the system and it could get you fired (source: fired someone for using one of these)
Yes, it's called mouse drifting. Basically, back in the early days of laser mice (which replaced the roller ball mice technology), the sensors weren't as advanced as they are today, so they would be "detecting" slight movements. When in fact, the mouse was stationary.
I think the only times I've ever personally dealt with that was when a wired mouse was slowly moving because the wire was dragging it. No idea about any other problems that could caus it.
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