If the bottle is open, then no, because the air inside of the bottle would push it outward to retain its shape just as the air outside is pushing it inward. This is the same reason why the atmosphere doesn't crush your lungs. If the bottle is closed, then yes, and the amount of pressure needed would be equal to the weight of a rock that would crush the bottle.

I don't know what you mean by a vacuum iron sphere - if the sphere is hollow, then yes it will be crushed, but if the sphere is solid, then no it will not by normal atmospheric pressure.

I will also note that funny things happen if the atmospheric pressure gets to the point where the air density is much denser than any matter you find on Earth. At pressures such as the interior of Jupiter, for example, the bottle and the sphere will be compressed, but won't lose their shape.

My 8th grade science teacher pumped the air out of a glass container and left it with a vacuum. It imploded, which means it collapsed in on itself. I didn't see it, but my science teacher liked to tell us about it.

Sure it can, depending on the shape and thickness of the iron sphere and the glass bottle. Iron is better against the vacuum compared to glass, but thin enough all of them could be crushed under the good vacuum. In short, there are three factors that are important against the vacuum: the material, the shape, the thickness.