Will gaming on my MBA 2013 generate enough heat to damage the cpu or the battery life?

I recently purchased a Haswell 13" MBA with the i5 CPU and 8 GB of RAM. I use it 95% percent of the time for work, and so maintaining the battery's capacity is very important to me. Right now if I'm writing on it with the WiFi off I can go two full days without needing to charge it, and I'd like to keep it that way.

That being said, I would like to do some gaming on it (WoW, StarCraft, Civ V). So far when these games are in use the fans kick in immediately and the computer gets very very hot. I know the MBA gets hot naturally when doing heavy lifting but I'd still like assurance that over long periods of time this will not damage anything. Also, if not plugged in the battery drops very quickly (an hour of WoW ate 60% of the battery).

Essentially I have a few related questions pertaining to heat and battery life, if you more knowledgeable lads and ladies would indulge me:

1) Will the heat from gaming damage the computer in any way, or is the heatsink built into the computer enough to handle these "hot to the touch" periods over time?

2) If the computer is plugged into an external monitor, and therefore closed shut, will the computer still be able to vent properly? Will the heat damage the screen if it is closed?

3) Would using a cooling pad with an external fan help at all, or could it interfere with the MBA's designed heat dissipation?

4) Will gaming while plugged into the wall (thus generating even more heat) damage the battery's capacity in any way?

Thank you all in advance for your helpful advice 🙂