Odd, you don't have any remote software like VNC running do you? Are you sure this isn't a sensor within the mouse going bad? Try using a different mouse and see what happens. Also, if this is a wireless mouse, try a wired one. Perhaps it's wireless interference.
Does the mouse just slowly creep to one side in a straight line, or does it actually move around the screen and try to "click" on items? If it just slowly moves, that happens from time to time with an optical mouse. I had one that did it almost every time the mouse was sitting still. If it is wireless, I agree with Hawkeye that it might be interference. A wired one should fix that issue.
I don't think so, as most times it is recommended that you temporarily turn off restore points when trying to remove viruses/malware as they can get backed up by the restore point system. Turning restore points off automatically deletes all current restore points.