OK, it is a big question. Let me try to answer it.
1. It's important to the whole transfer function of the power stage and will determin the compensation design. (Bandwidth is directly related to transient response)
2. The ESR will help the stability but will generate more ripple. For old Non-linear controls, this ESR will generate ripples which is necessary for control
3. For computing power system, VR12 have detailed information about the output capacitors.