My understanding, as an experienced referee of soccer/football at many levels, of the way that suspensions are determined (in Australia at least) is that all the factors you have mentioned are considered against prior cases as precedent for punishment.
In Australian sports at many levels of professionalism, these decisions are specifically made by lawyers specialising in interpretation of the Laws of the Game (or equivalent for a given sport) and competition rules. This is intended to remove prejudice or biases from the decision and remove the sports governing body (such as the FA) from the process.
In this specific example, the review committee might look at factors such as malice, force or intent. While there is no excusing Núñez's actions, they would have been objectively worse if, for example, he had held Andersen's head and directed his headbutt more directly into his face, or followed the initial strike with one or more subsequent blows.
As for procedures, as far as I am aware, these are specifically held in confidence by the reviewing bodies, but can be assumed to be fairly similar to regular courtroom trial, albeit without a jury.