It's like that meme with the shop of cursed items but now most of those drawbacks are just a regular part of our society. The Fae aren't much worse than the rich people we already have (except the aggressively carniverous portrayals) and at least they tend to be right there in front of you so you can hit them with a brick or something.
iirc some mushrooms do that without the corpse - the main mushroom is in the center underground, while the fairy ring is basically the fruit it produces (these are probably not the correct words to describe this - but thats the principle, I think :D)
The mycelium is the main body of the fungus, yes, and it's the entirety of the circle. The mushrooms on the edges are indeed the fruit.
And it's every type of mushroom that does this... sort of. Any mushroom that grows along the ground at least. There are plenty of varieties that grow on trees and throughout a leaf pile or such.