Has anyone "repaired" the amphitheather? I'm wondering if this is even something that happens in the game.

I also would like to know if anyone has come up with a use for the "pile of loose stones."

The Ampitheater doesn't need to be repaired. Unless after it rains, it needs to be cleaned.

No, the amphitheater stay like that but there is mod (modification) I think. When you're in the Forum List, scroll down to the bottom and look at the Mod section.
And the pile of stones stay here also, "we never know", it could be useful!! (as a lot of stuffs in my home!!)

(SPOILER ALERT):


I always thought the "loose stones" could be useful in the lift so as not to have to wait for it to rain to get those first few "seeds" for the orchard. When I was first playing and fixed the lift, it was the first place I took a villager in the hopes of getting them to put one of those rocks in the bucket on the lift. Made a lot of sense to me . . . Still don't know why it shouldn't work. They can carry those rocks all over the village and up the path when they exercise. Maybe they're too big to fit in the lift?? (But you'd think there'd be smaller ones somewhere in the area.) And why couldn't they use water from the waterfall for the lift?? They can carry it to the fire, when needed.

But, alas, those rocks are destined to sit in a pile and be forever "loose rocks."

On a similar note to CaveDweller, I at first thought that the lift should be used in some way to collect the "hanging thing" and wasted a lot of time trying to move the lift with various combinations of villagers, to no avail, of course.

And I thought the red and blue hanging "ornaments" would be involved somehow. I'm still not sure what they are (berries? cherry-blueberries? certainly don't look like anything from a mango, banana, or papaya tree!) But somehow I suspect that it was designed to do just what it did -- confuse us all!

They use stones from the pile to repair the bath. but it stays there still so???

They take them from very NEAR the rubble for repairs. The rubble is a different puzzle all by itself.