"Derivation" of Minkowski metric? Is there a deeper meaning behind the the Minkowski metric?
Does it just come from the SR formulae? Or is there some deeper geometrical meaning, maybe in the context of GR? 
 A: If we restrict ourselves to special relativity then the form of the Minkowski metric is an assumption. You can argue whether it is derived from the Einstein postulates or whether the Einstein postulates are derived from it, but this is really a philosophical nicety as you end up having to make equivalent assumptions either way.
If you consider general relativity then the Minkowski metric is derived in the sense that it is (one of) the solution(s) to the vacuum Einstein equation. I suppose the next question is how the Einstein equations are derived, and again this is a somewhat ambiguous question. I would guess most relativists would regard the Einstein-Hilbert action as the fundamental assumption from which general relativity and therefore ultimately the Minkowski metric is derived.
A: In general relativity, the Minkowski metric plays a privileged role because it is the unique asymptotically flat solution to the vacuum Einstein equations that has zero ADM energy. The positive energy theorem in general relativity says all asymptotically flat spacetimes satisfying the dominant energy condition have non-negative ADM energy.  Thus, one can think of Minkowski space as the true vacuum state for (asymptotically flat) general relativity, since it is the state with the lowest energy.  
