You want an aftermarket cooler like the Hyper 212 evo.
You don't want any PSU described as an "OEM blah blah blah watt", it is almost certainly garbage. Even a decent cheap 430w like the Corsair CX430 will be far better. Lots of other quality Power supplies but they all are 80 plus certified. Some good brands are Seasonic and XFX.
Note that an i5-3570k & z77 motherboard would be a better gaming system and a better overclocking system for similar money, but what you have now will definitely work together.
Quality 430 watt can handle that build. Probably has more 12V power than the "600" watt OEM power supply.
1gb = 2gb card in terms of FPS unless textures get too big. In practice in current games that almost never happens except at very high levels of Antialiasing or at resolutions higher than 1920x1080. I say that having a 7850 1gb and playing Far Cry 3, Skyrim, BF3, etc no problem. IMHO when 1gb gets to be too little it will be time to upgrade anyway. If you don't plan to upgrade for >2 years then maybe get a 2gb one.