Depends on the heatsink. Most can be removed by a few clips or screws on the side. Make sure to re-apply thermal paste before putting back your heatsink.

Normally a CPU doesn't need a cooler (most already come with what they need), if you don't mess with it. If you do decide to overclock the CPU, that's when an extra cooler might be needed. Overclocking might make the computer a bit faster, but only those who live for boasting that they play such and such game at 130 FPS really notice a difference (and only because the benchmark software is telling them so). You can play all current and future games in that CPU without a problem, and if you don't want it for games but for serious applications, then you shouldn't be overclocking the CPU in the first place.

First of all make sure that your case is geting cooled okay, because you can't cool your processor much, if your case is hot.

A CPU cooler is anything that cools the processor of a computer. Usually, this is a fan and heatsink, but many people also use water cooling, and some even use mineral oil. Between the heat shrink and the CPU their is usally a thermal compound in place to dissipate the heat faster by allowing even distribution over the heat shrink. This means that the fan can now blow this hot air away from the CPU, allowing it to operate more smoothly. Hope this helps.