I think its the other way around, the stock cooler dislikes the CPU. Well I think the 2600 ones have turbo boost to 3.8GHz, so I have seen people do slight overclocking to make their base clock 3.8GHz on stock cooler.and since the 2600 normal and k versions dislike the oem cooler, i don't think you want to do anything with it with the original cooler, many people have overheating issues with it.
You can see on computer properties(right click in computer on start menu then click properties) if it's 2600 or 2600k.
2600 = locked; cannot be overclocked
2600k = unlocked; can be overclocked
That is not true. 2600 can be overclocked but it has limited overclock.
2600K is the unlocked overclock. Also I wouldn't let CPU go over 50 C if i were you. So be sure you have good thermal paste and good heat sink.
Sandy Bridge CPUs are good up until around 80 degrees. Past that, they start to lose performance and downclock themselves.
80 C is too hot for CPU.
For an AMD one, yeah. Depends on the model.