I later successfully rotated the monster around by having the pivot point at the origin but that got me questioning how the monster was not distorted since it wasn't perfectly align with the x-axis (the mirror modifier). An example is here below where the monster is not aligned with the x-axis (mirror modifier) but still in tact, how is this possible? It got me more confused when people started associating the axis of the mirror as the symmetry of the object mirrored since it seemed to contract my photo below. Can someone help explain this?
If I understand correctly your question, it looks like you're confusing Global orientation with Local orientation. The Mirror modifier will mirror the mesh on the object's local X, Y or Z axis, not on the global X, Y or Z axis. So for example, if you mirror on the X (local) axis, here is what you have:
If I come back to Object mode and rotate the object on the Z axis, it won't mess up the mirror because my rotation was in Object mode and didn't affect the mesh on its own local axis. Here I've enabled the Transform Orientation display to make it clear, it displays the object own local orientation, you can see that it follows the object rotation, so the mirror effect won't mess up the mesh.
But if I come back to Edit mode and rotate the mesh on its Z axis it will mess up the object because this time I'm in Edit mode and the Mirror modifier takes the mesh local orientation into account!