It's called a 'nipple' or a 'track pad pointer' or even a 'red cap', You can get replacements in a few places if you search for the above terms.
Regarding the moving mouse pointer, it could be a virus infection - yes seriously, it could be someone's deployed a trojan on your computer and is using it unaware you're also using the computer at the same time. Or it could simply be a 'gag' have you let any mates near your computer recently who may have deployed a 'gag program' on it? Are you sure that you've installed the correct drivers for your nipple\trackpoint etc or have they been 'upgraded' incorrectly, if so then maybe you could just use the system tools\system restore option to get it back to a working state?
Or perhaps you're using the 'fn' key and some 'directional keys', in which case you'll just need to turn it off by depressing the 'fn' keys again.
Here's some gag programs:
http://www.google.com/search?hl=en&q...earch&aq=f&oq=
Here's some replacement nipples, trackpoint caps etc:
http://laptopbatterymall.co.uk/new-2...21-p-1293.html
http://www.clickykeyboards.com/index...arentcat/13112
If none of the above is applicable, you could try clicking each of the keys on the keyboard one after another, see if one of them is stuck. Alternatively, you could try disconnecting anything and reconnecting whatever the mouse is you're presently using.
If none of the above don't solve teh issue, I must admit to being out of ideas. Perhaps it's something native to the operating system? Perhaps the System\System Restore option maybe a way to go if it's available to you, pick a time\date when the computer was working last and then back the computer upto that date.
HTH