Intel(R) Graphics Media Accelerator X3100, can it handle Pixel Shader 3.0, and Hardware Transform and Lighting?

You are going to be disappointed with the performance of that integrated graphics solution with just about every game on that list. I suggest you get a real video card. The Nvidia 9600 GT can be had pretty cheaply. If you're on a laptop, there's not much can do though.

Just what it says intel is the manufacturer of the video and audio chip set on that board. The memory is shared with you RAM memory. So if you have 1 gig RAM memry for the laptop than 358 is allocated if needed for the video memory. The graphic media accelerator X3100 is the model of the video card that is manufactured by Intel. This is common on most laptops they have integrated graphic and audio cards into the motherboard.

Intel(R) Graphics Media Accelerator X3100, can it handle Pixel Shader 3.0, and Hardware Transform and Lighting? No

Intel® Graphics Media accelerator 3100 (Intel® GMA 3100) has support for Microsoft DirectX* 9.0c, Shader Model 2.0 and OpenGL* 1.4.

Currently, only the Intel® G35, G43, G45, G965, GL960, GM45, and GM965 Express Chipsets support hardware Transform and Lighting (T&L).