Seems Intel is only focused on putting out a quality cpu, but only gets the job ½way done. The paste used between the IHS and IC seems to have been installed by a blind chimpanzee. Has been this way since the switch from soldered IHS to paste with Ivy-Bridge lga1155. Consequently, temps per core are always funky with averages around 10°C between hottest and coldest cores and a hotter running cpu. So ppl took to de-lidding, where the monkey crud is removed and a higher quality, more efficient and cleaner installed paste is used to replace it. Correctly (you hope). End result is a general evening out of the temp variances and a slight lowering of temps across all the cores. This doesn't affect the IHS in any other way. You still see the Intel factory print on the IHS surface.
Lapping/polishing is different. Can be done on either unlidded or delidded cpu. Because of manufacturing, the IHS is never perfectly flat, it's got a slight bow in the middle, making external paste thicker generally in the middle. Common theory is if you polish/lap the IHS surface, basically grinding it down to flat with sandpaper, you'll get a better, flatter, more even compression of the external paste to the cpu cooler. The result if done right is an almost mirrored surface to the IHS, however, this process totally destroys the factory print and invalidates any warranty or possibilities of guaranteed identification. It's quite often done to engineering prototype cpus which are illegal for sale if identified as they are Intel property that's basically stolen. So don't buy lapped/polished cpus unless you know for a fact the history of the cpu.
1. Don't bother with AS5 it's a very mediocre paste to start with and needs to be often replaced as it only has a 200ish thermal cycle (from cold to very hot) averaging a yearly change on OC cpus.
2. No, you absolutely need the IHS or the distance from cores to cooler is changed and any paste used totally bunks up the cores themselves making cleaning old paste impossible.