To answer your questions:
To remove the cooler, it is best to run the cpu a bit before so that the paste will soften and make it easier to remove the cooler.
Yes, turn the pins counter clockwise to unlock them.
Leave the cpu in the socket; no need to remove it. To remove the old thermal paste(as you must) use something lint free like a paper coffee filter. cloth or tissue can leave lint.
Rubbing alcohol will do the job. It dries almost immediately so nothing special needs to be done to dry it.
Once you have remounted, you can use it immediately. Over the period of an hour or so, the new paste will spread under heat and pressure.
Do not use too mush paste, or it will act as an insulator. A small drop in the center of the cpu die is all you need.
It is hard to use too little.
Here are my stock instructions for the process:
----------------how to mount the stock Intel cooler--------------
The stock Intel cooler can be tricky to install.
A poor installation will result in higher cpu temperatures.
If properly mounted, you should expect temperatures at idle to be 10-15c. over ambient.
To mount the Intel stock cooler properly, place the motherboard on top of the foam or cardboard backing that was packed with the motherboard.
The stock cooler will come with paste pre applied, it looks like three grey strips.
The 4 push pins should come in the proper position for installation, that is with the pins rotated in the opposite direction of the arrow,(clockwise)
and pulled up as far as they can go.
Take the time to play with the pushpin mechanism until you know how they work.
Orient the 4 pins so that they are exactly over the motherboard holes.
If one is out of place, you will damage the pins which are delicate.
Push down on a DIAGONAL pair of pins at the same time. Then the other pair.
When you push down on the top black pins, it expands the white plastic pins to fix the cooler in place.
If you do them one at a time, you will not get the cooler on straight.
Lastly, look at the back of the motherboard to verify that all 4 pins are equally through the motherboard, and that the cooler is on firmly.
This last step must be done, which is why the motherboard should be out of the case to do the job. Or you need a case with a opening that lets you see the pins.
It is possible to mount the cooler with the motherboard mounted in the case, but you can then never be certain that the push pins are inserted properly
unless you can verify that the pins are through the motherboard and locked.
If you should need to remove the cooler, turn the pins counter clockwise to unlock them.
You will need to clean off the old paste and reapply new if you ever take the cooler off.
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