How can gravity truly be infinite? From my knowledge, gravity is infinite and extends throughout all of space. It diminishes as distance increases but is still present everywhere. So given enough time, no matter where something is in the universe, it would accelerate due to the gravitational force of something in the universe.
Also, from what I know, the Planck length is the smallest possible length.
But if gravitational acceleration is X*meters/second/second and this force decreases with distance, wouldn't you eventually after some distance reach a point where the "X meters" would be smaller than a Planck length and therefore the acceleration would be nothing? Because on object can't move less than a Planck length if it is the smallest possible length. And therefore wouldn't gravity have some sort of limit and not truly be infinite?
 A: 
From my knowledge, gravity is infinite and extends throughout all of space. It diminishes as distance increases but is still present everywhere. So given enough time, no matter where something is in the universe, it would accelerate due to the gravitational force of something in the universe. 

You must mean "the effect of gravity reaches to infinity" .
This is in classical mechanics, the law of gravity 

We then have General Relativity, 

General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 19161 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present.

Still classical physics up to here.

Also, from what I know, the plank length is the smallest possible length.

The Planck length is in the domain of quantum mechanics, ( h_bar is zero in classical mechanics) not classical mechanics. It is not the smallest possible length, since mathematics has no limits on variable sizes. It is a length small enough that the physics we know is undefined for lengths smaller than that. 

And therefore wouldn't gravity have some sort of limit and not truly be infinite?

The force of gravity is mathematically infinite  at r=0 according to the classical law of gravity. You mean that the effect of gravitational attraction should be limited at very large distances, though I do not understand your formula . It is at r=0 that quantum mechanics will take over and avoid the infinity, not at very large distances.
One will be able to talk of the relation , if any, of the Planck length to the law of gravity once one has a definitive quantized gravity theory, which is still a research topic. 
A: It is not so clear what you mean by "infinite", but maybe you mean to ask why gravity has infinite range. It comes from the fact that the force of gravity decreases as $1/r^2$, thus slow enough for it to be felt by objects at the other end of the Universe. The same property is seen in the electrostatic Coulomb's force that decreases as $1/r^2$ as well.
This is not the case of all the forces. For instance, Coulomb's repulsion between electrons in solids gets screened because of the presence of other electrons, and can be modelised by a potential of the form $\exp(-ar)/r$ instead of the usual $1/r$. This potential is said to be short-ranged as it cannot be felt by two electrons far away for each other ($\exp(-ar)/r$ decreases much faster than $1/r$).
A: Gravity, Itself acting like a property in space. But, It can be only infinite when at r=0 you have, 
m=more then schwarzschild radius. Then only you can achieve the infinite gravity. 
At the very event horizon of a black hole, The spacetime changes its values and time tends to zero where space tends to infinite. By that equation, I think space is directly propotional to gravity.
