What is the easiest way to add/extrude an edge loop around the hole in the first image to make it like the second image?
Select the loop, and CtrlB bevel it, with 2 segments, and a profile of 1. This will give you a bevel with the original loop intact, the new loop you want, flush to the outer surface, and one you may or may not want around the recess. You can CtrlX dissolve the inner one away, if you like.
You can follow this up with a GG slide on the new loop(s), using E to make the slide parallel to one or other of the surrounding loops, and F to decide which.
Select your hole (the cylindrical edge loop) completly and press E and S to scale. Press Shift + Z once or twice to contrain the scale axis correctly. Then type in the amount of scale you want and remember it. Next press Numpad + and scale by 1 divided by your remembered scale. You may need to take out an calculator for that. Hope this workflow helps you