: There are two fundamental reasons that the theory of the existence of black holes will eventually be proven in error.

This is improper use of the word theory. There is no the theory of the existence of black holes. There is the theory of general relativity which was used to predict the observational discovery of black holes.

:(1) A hole, by definition, is devoid of matter.

That's not the definition of "a black hole". That's the definition of "a hole". These holes are two different words with different meanings.

:(2) The force of gravity would have to be applied in only one direction (inward)

That's not true.

:but as we all know it exerts in all directions. Consider the following....

Not exactly. In a Newtonian limit, superposition accounts for this.