so this will be like shadow hunting, once you start you see them everywhere?

Yep :D

They are called cherry mushrooms?

Oh no, its a made-up name :) Soulsdetour found them a few times near her cherry tree and you mentioned they grew there too. I found similar, or the same near apple tree. But the "cherry mushroom" name is more catchy :p
They seem to really like fruits.

But now that I looked again at mine, they are different...