Is it correct to assume that the relationship between an objects mass and size, is what decides if it’s a black hole or not? I’m asking this question in reference to a scenario I saw posted a couple of days ago, where it’s stated that if you would shrink earth to the size of a cherry, it would become a black hole.



Is it also correct to assume that changing the size of earth while maintaining the mass, will not affect objects which are further away than the event horizon?

I’m asking this in reference to the same scenario as above. It is also said that changing the size of the earth, so that it becomes a black hole, will have no effect on the orbit of objects around the earth - e.g. the moon.

I’m trying to understand this, with an image of how much the earth will bend spacetime. Both as a earth-sized earth and as a cherry-sized earth.
Yes. A black hole is in some ways a very simple object. It has mass, charge, angular momentum. 

These three values determine the size of the event horizon. If the Earth's mass were compressed to less than the size of a cherry it would be inside its event horizon and so would be a black hole.

The gravitational field of the Earth out at the moon would be (almost) unchanged. The moon would orbit an Earth-mass black hole in the same way that it orbits the Earth now.  The small differences are due to irregularities in the shape of the Earth, which wouldn't exist if the Earth were collapsed.

Above the Earth's surface the curvature of space would be (almost) the same if the Earth were to be collapsed. If a rocket were to use its thrusters to hold itself stationary 6400km above the black hole, the inhabitants would experience 1g of gravity, just as we do standing on the surface, 6400km from the centre of the Earth.

If you go far enough below the Earth's surface, gravity weakens, because there is mass above you.  If you collapsed the Earth, then gravity (and curvature of spacetime) would increase all the way to the black hole.