I never had mushrooms in my garden. But this year they appeared in a significant number. Why?
They appeared in the area where a large tree was removed last year. That area was generously watered this year (to support new plants). Could that be connected to the mushrooms?
They're a perfectly natural part of nature's disposal/decomposition system - they break down dead wood. If they didn't, that dead wood would take forever to decompose, so if you have woody roots or even a stump left behind, fungal activity is an obvious consequence. The fact you've watered the area assists the fungal process and will aid faster breakdown of the dead wood under the ground.
Most of the fungal growths associated with decomposition are harmless to other, living plants, but there are one or two that you don't really want to encourage in the garden, honey fungus being one of them. However, you've not described the growths, but given they're fruiting now, its less likely to be honey fungus - they fruit around September. You do not need to remove the mushrooms unless you just don't like the look of them - the mycelium that supported them will still be present anyway, and will continue to do their work on the wood.
Yes. Probably it is some Armillaria, but maybe other species. Fungi likes dead wood (and dead roots) as nutrient to grow. Fungi cannot produce own food (evolutionary, they are more related to animals than vegetables), so they need to find nutrients.
You should remove them, and in a few years they should reduce, until they will find no more root. Next time, when you remove a tree, try to remove as much as possible his roots (especially root near surface).
If you are lucky, the fungi are on another species, which like just the chips (produced by cutting the tree). In this case chips will disappear a lot quicker.
