On the infinite range of the electromagnetic force I am curious as to whether there is a fundamental reason why weak and strong nuclear forces have such a short range whereas gravity and the electromagnetic force seem to have infinite range. 
Since gravitons stand undiscovered, I'll talk about EM forces alone.
A couple of answers suggest that the infinite range of electromagnetic forces is due to the masslessness of photons, and I'd like to know how. It makes me wonder if this conclusion can be directly drawn from Maxwell's Theory, or whether this is related to the form Coulomb's Law takes due to more fundamental reasons related to this fact.
I am a second-year undergraduate so I request you to frame an answer keeping that in mind. Thanks:)
 A: This is only an answer to part of your question:

A couple of answers suggest that the infinite range of electromagnetic forces is due to the masslessness of photons, and I'd like to know how. It makes me wonder if this conclusion can be directly drawn from Maxwell's Theory, or whether this is related to the form Coulomb's Law takes due to more fundamental reasons related to this fact.

The infinite range of the Coulomb force indeed follows from Maxwell's theory. From the equation
$$\nabla \cdot E = \epsilon_0 ^{-1} \rho$$
you can derive that the electric field from a point charge $\rho(\vec{r}) = \rho_0 \delta(\vec{r} - \vec{r}')$ decays as a power law $|E| \propto |r-r'|^{-2}$.
As the Coulomb force experienced by a stationary test charge $q$ is $F = qE$, the Coulomb law follows directly from the above in Maxwell's theory.
The fact that the field decays as a power law, rather than exponentially, is what is meant by the infinite range of the Coulomb force. I don't know enough about the nuclear forces to comment on why they behave differently.
