Subdivide edges vs Collapse Edges vs Subdivide Collapse. An example for each method?

Well, the situations are way too broad and arises all the time to be able to give examples tied to specifics, but I can say this in a simple way:

Subdivide edges -> You need resolution because you have to nail a small detail. It preserves and amasses details. 

Subdivide collapse -> It's an eraser of sorts, if you're not happy with a detail, wipe it out. It'll squash details. 

Collapse edges -> No one uses this, it's like Hawk-Eye to Blender's Avengers. 

This kind of question has been asked before, it's perfectly normal, but I think the premise is ill-advised to begin with. It's enough to know the function of the tool, after that, wanting to control too much is all dead weight. It's like a pencil in your hand, you're not preoccupied in advance and aware of where the next stroke is going to go or what the exact pressure on the paper should be, you're just feeling it, you're just drawing on the fly. Same for this, I'd say try not to think too much of the technical, you don't have to control every little aspect, it's enough to understand it and then just have it a go, you'll adapt and readjust by feel as you go on. You'll start to get the feel when to use each method and change to one or the other, you wont have to even think of specific situations or be in alert to them.

I always get reminded of The Last Samurai, when Tom Cruise was trying to beat the other Samurai in Katana practice and he isn't able to, and that other dude comes and says "No Mind, too many minds watching" and Tom is like oh, I'm too hung up on the extra attention and my mind is scattered. He then focus only on the guy in front of him and forgets about the world and he beats him.