Obscuring / not rendering parts of an object on camera

Hello, I'm new to unity, Im wondering how could I hide parts of an object, like a mask, for instance, could I have a sphere and only render the part of the object inside the sphere, so that whats outside the sphere does not render, while at the same time, not rendering the sphere itself. So in essence, the sphere normals would be turned outside in (like a dome) and any object in contact with the sphere would only render inside of it.

As an addition, would it be possible to simulate some type of "fog" masking, like poka dots, in the edge where the objects cross the sphere? So that they're edge is just not "cut off" at the maskign point, but rather they would just fade away (parts of the object).

I would definitly consider a small monetary compensation to anyone willing to help me achieve this. Thank you