My answer to question #3 is the Cooler Master Nepton 140XL closed loop liquid cooler for $99. Even if you are not overclocking it will keep your CPU very cool, quiet, and extend the life of the CPU
I will answer question #2. I am looking at building a similar rig and I have decided on the ASUS M5A99FX PRO R2.0. Best budget performance board for FX CPU's
Do yourself a favor, and save a little money by purchasing an AMD FX 4100 CPU, and an Asus M5A97 R2.0 socket AM3+ motherboard, as well as 8 GB of 1600 mhz RAM. Pair that with an AMD Radeon HD 7970 GPU, and you should be able to play any game in max settings. (1920 x 1080)
On a side note,(still APU related)I successfully overclocked the AMD A6-3400m APU in my Toshiba Satellite L755D-S5218 notebook from 1.4 ghz(stock) to 1.8 ghz w/ a boost of 2.3 ghz using stock voltages. That's a 25% overclock :)