How well will my new laptop run my games?

Quite bad:
http://www.notebookcheck.net/AMD-Radeon-HD-7670M.69483.0.html
There you have a full list of games on that GPU and their FPS.
You are very funny btw.

PS; http://www.notebookcheck.net/AMD-A-Series-A8-4500M-Notebook-Processor.74884.0.html

The CPU is on position 205 ranked on mobile processors just at the same level as a Intel Core duo P8400, and thats a old CPU (but not of the slowest ones).
So in general, that laptop is a poor performer (but for that price its kinda normal).

Assuming your CPU dosent burn from the heat, maybe it can use the coressifre setting:

http://www.notebookcheck.net/AMD-Radeon-HD-7640G-HD-7670M-Dual-Graphics.81172.0.html

 
The A8-4500m is not too bad. While the base speed is 1.9GHz it can reach a max of 2.8GHz assuming only one core is being used and the temps are not too high.

For the price, the Radeon HD 7670m is actually pretty good. It is certainly not the highest performing graphics card, but then again you are not spending over $1,500+ for a laptop. In general, you should get pretty good performance in most games using medium quality settings.

In graphically intensive games like Hitman: Absolution and Metro 2033 you will wish that you spent more money on a laptop with a high end graphics card, but you didn't list those as potential games you want to play so you should be okay.
 

GMPoisoN

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It will run all of those games just fine as long as you don't try and max out any settings. I run WoW on a laptop slightly worse than that ($1000 a few years ago) and I can play with everything in medium, minus shadow effect.