Do you have a trackpad that you can touch to click a button? If so, deactivate that feature.

This is all in the same area of the notebook which makes me think that perhaps your issue is some sort of loose or haywire connection between the touchpad and the motherboard.

This doesn't sound like a software issue, but if problem 1 goes away after the deactivation of the touch-to-click feature, write back saying so.

I'd take that machine in for servicing, it sounds like it needs to be opened up and examined.