Don't use paste with stock coolers. Or any cooler. Since you have such a beefy CPU, buy a Hyper 212+ or a cooler like that, and buy a tube worth of either Arctic Silver 5 or MX-4, good stuff. And no, thats not a CPU cover for protection - all modern Intel sockets have that because it hold the CPU down, connecting the pads of the processor to the pins of the board - it's needed to secure the processor. And yes, all you have to remove the lid on the cover, open the cover, put the CPU down, place the cover over it, secure it, and then put a REALLY thin, short, vertical line of paste on the processor over the die - this will ensure the best cooling operation.