|Find a working usb mouse but don't plug it in yet.|
Go to Control Panel >> Mouse >> Click 'Device Settings' tab.
Tick the box for "Disable internal pointing device when external mouse is attached".
Now plug usb mouse in & wait for it to be detected.
If those problems no longer exist, it's the touchpad or it's driver causing them.
If you have drivers available, re-install the "Synaptics Touchpad" driver which may cure the problem.
After re-installing touchpad driver, remove the ordinary mouse and restart Windows. Check for the problems again.
Unfortunately, the HP website (both UK and US) do not have a touchpad driver to download for this model , I just checked.