No. It was a very sneaky tree.

Yes. This version of reality (existence) was designed to be rendered live and on the fly without limitations. Therefore, everything has to be up and running all the time, even when not observed. Even millions of light years away, there's a rock on a planet that sits there everyday while you do people things. It exists just as much as you do. The universe is the display, the hardware, the coding, and you in the seat, all at once. Now that's what I call omnipotence. I'm pretty proud of it.

No because that would be unnecessary computation, but a fast calculation on the physics and collisions will be done so its is save to say "the tree fell" because we can observe the results of said fall

It depends on if any players, or sound aware NPCs, were near enough to it that it may matter.