This is quite approximative. The problem with gravity is that it's often confused with what we "perceive" as gravity on earth, which is quite an extreme case.
"If an object has a larger mass, it will "pull" other objects towards it."
The force is actually applied to both objects in the same way. The heavier object would move less because it will accelerate less (F=m*a), but both objects would be pulled toward the global mass center.
"The strength of this pull is directly affected by the size and mass of the matter of the central object."
The size have no place in gravity (if you replace the sun with a dot of the mass of the sun, we would perceive no difference in terms of gravity), it simply determines where objects will bump each others ;)
"Gravity is theoretically a constant"
Gravity(its acceleration) is approximated as a constant when considered as the strength applied to a body on the surface of the earth (9.8 m/s2), because the variation in the distance from the center of the earth and the mass of the body is negligible, but its not a theoretical constant. The gravitation "constant" G is just a factor to make the formula (F=G*m1*m2/r2) works with our measure system. Gravity can be modelled as a field, which means it has spherical symmetry, so yeah at the same distance you will have the same strength, but that's quite an approximation if the bodies are comparable in mass and/or not spherical.
I know I'm probably being too fussy but the name of the game is space engineers dang :D
Artificial Gravity Acceleration
I've found that acceleration of a ship due to artificial gravity and artificial mass follows this equation:
[Acceleration of Ship] = [Artificial Mass] / [Inertial Mass] * [Acceleration due to Artificial Gravity]
I was hoping someone could make this look all pretty on the main page as it is super helpful for designing gravity based systems. :) - Whiplash141