1. What kind of modifier is 'well established as early as the eighteenth century
-- its a ed modifier -- in the given phrase which word occurs as dominating? 'established' -> this could be the head word.( I am not providing any rules here; just a technique)
'well' - adverb modifying established;
established -- acting as adjective; think of well established company, well established technique, method etc.

2. Is it necessary to have a comma before 'well' for this statement to make sense
the sentence is still ambiguous whether you have comma or not.

Being a adjectival phrase it has tendency to attach to closest noun whether you have comma or not.
particularly,in this example noun 'method' two levels away( of ...of..) from the modifying phrase.

The intended meaning is 'method well established as early as...', but in the sentence it could mean - 'minerals well established';
So the sentence is still ambiguous whether you have comma or not.

Note that you don't need to know whether its a ed modifier or not; Just check, how the group of words
minerals well established' blended in together; so there is a potential ambiguity of meaning here.

if the sentence has 'method of extraction well established..', there is no ambiguity.


One reason why a comma is used is to separate non essential modifiers.So, question your self 'well established as early as...' is an essential modifier or not?
From the meaning of the sentence- well established is needed, so without comma is a better option.