Based on HP's website for the HP Pavilion G7 is a custom laptop that supports the 2nd generation Intel® Core™ processors including the Intel Core i3, i5 and i7. So yes you most likely would be able to upgrade the processor on this unit to an Intel Core i7 (to be sure check with HP to ensure that the board they use does support the replacement processor you are looking at).
The website lists the graphics as the Intel HD 3000 Graphics that is used on all of our 2nd generation mobile Intel Core processor. While you can dedicate more memory to the graphics you really can't replace a card in a laptop.
Christian Wood
Intel Enthusiast Team