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1) What kind of battery life can I expect out of a high performance laptop. (3.6Ghz, 6800/7800 GPU)
2) What kind of cooling problems will i run into with those high end components.
These are directed to an alienware Area-51 M770 with those components installed.
Based on my experience with an older Area 51-m that was 2.8ghz and R9800 Pro, I wouldn't expect to get much done on battery, if you try to game it won't even last an hour. It'll get really hot, you won't want it on your lap. Even though it gets really hot, it should be designed to handle it, so you shouldn't have to worry about it.
With a Pentium4 or Athon64 CPU, you can expect around 45 minutes of battery life. A Dell desktop replacement laptop, that uses a Pentium-M CPU, can get between 1hr30min to 1hr45min of battery life. Desktop replacement laptops were not really designed for mobile use. Think of them more as "moveable" desktop computers.
The design of a laptop should come with enough cooling as-is. You should not have cooling problems (though the laptop will run very hot).