The dream is that the “true physical theory” will give a prediction for these numbers.

In string theory, the forces are envisioned to be higher dimensional extensions to the usual 4-spacetime. Compactifying these higher dimensions to 4-spacetime produces a solution for the fundamental constants. The problem is that there are many ways to compactify higher dimensional spaces to the usual 4-spacetime, and each one generally produces a different solution for the fundamental constants. For 10 dimensional string theory, there are ~10^500 ways to do this. This is known as the *string landscape*.

It is still a subject of research whether we can find our universe within the string landscape. Note that while the number of solutions of physical constants (the jargon in the field is *vacua*) is dauntingly large, it is not infinite, which is a good thing.

No, these fundamental dimensionless physical constants are all independent of each other.