The repair method you're asking about is called darning! If you've got yarn leftover (or even just yarn in the same weight class), you can patch the holes without needing to take the socks apart. This article explains how to do it and you can get darning eggs on Etsy but I've also seen tennis balls recommended. Anything that you can use to hold the sock like it's being worn while you're working will do it. Sock darning tutorial's over here.
If/when the heel wears out, you can also replace it with an afterthought heel I use this method once in a while for different colored heels instead of doing a heel flap/gusset. You can also use this for different colored toes and repairing them as they wear out. How to do an afterthought heel For doing both of these, I'd recommend putting in a life line on the row of stitches below what you're removing to hold the rest of the sock while you work. (Any contrasting sock yarn or thin nylon cord would work fine for this).