A horizon only exists as block in the field of vision. For example, I can't see my neighbors house because of the fence between us. To see the house, I raise my self on a chair, and force the horizon to be LOWER.

On a flat earth, with flat topography, the horizon and the infinite point are the same thing.

Nothing would dip below the horizon, because there is no obstruction.

Perspective does not cause dipping below a horizon.

On a spherical earth we'd expect a "mountain" to form between you and an object you are moving away from. This mountain is the curvature of the eartg. The top of this mountain is called the horizon. As you move away from object, the mountain grows, obscuring the bottom of the object.

The reason I can't see Paris from my house is because of this mountain. Slice this obscuring section off the Earth, and I'll see Paris with a good enough telescope.