-If I upgrade my graphics card to say the MXM-III does this mean that I get to use the on board and the new graphics card combined as one to make a 512MB graphics card?
You cannot upgrade to MXM-111 only MXM- 1 or 11, from post #4
your computer will accept the 1 and 11 type but not the 3.0.
Having both an onboard video chip and an add on video card does not mean that they combine, the add on card normally overides the onboard chip.
-Would I have to buy an external monitor or would It connect directly to my touch screen monitor that is built into the HP touch-smart?
No to the 1st question and yes to the 2nd question.
-Is there enough space in my computer for the new card to fit and the back and would I have to drill any holes for wires? (I know this question sounds stupid, but like I said I'm not so good with hardware)
Yes to the 1st question (see the picture below for what MXM cards look like) no to the 2nd question.
-And lastly could you please point me in the right directions as to which card to get, because you are unsure of which MXM card I can use e.g.(MXM-1 or MXM-3) is there a way I can help you help me in figuring this out?
Google MXM cards, make sure you choose the version 1 or 11 type and that the card is not bigger than 70mm X 68mm in size, this is why the version 111 type of card is not compatible, it is too big.
Finally when you find a card post a link to it so it can be checked for you, I will also search for you but it may take until tomorrow to find one.