Yes, all AMD or Intel processors that are BOXED come with the 'Standard' heatsink & Fan combination. However I, like many gamers, do not use them & pay from under £20 UKP for a better cooler, or Freezer to cool their CPU's as Gaming, along with any other high end users, like film producers, Graphic designers, etc. as the 'regular' ones do not cool as well thus a better cooler prolongs the health & life of the CPU.
Hope this helps :)
With the most basic of heatsinks, yes.
Yes, but a very simple metal finned type, no copper or heat-pipes, and a small fan. I wouldn't even think about overclocking with them, as under load it gets to just almost 10 degrees of it's "thermal margin" according to AMD overdrive software.