I'm new to this and I don't know how to do quotes yet. Stuff from the OP will be bolded.
In this unnamed Magical system, there are:
Fire, Water, Air, Metal (Mineral Aspects of Earth), and Wood (Organic Aspects of Earth).
First off, I like the fact that you divided Earth into its mineral and organic components. But were is the cutoff? Is dirt considered organic or inorganic. How about fossils? Seashells?
These Five Elements can be combined in a pair along with one the the Five Essences:
Mind, Body, Spirit, Life and Death(Or other 5th Essence).
I don't feel like I can make many comments on these without more info. Could you give more details on them?
A Homunculi is an Artificial creation - a living being held together by colliding the three essences/elements together, and constantly maintaining the creation with "Life" Essences.
A normal living being has an innate amount of life essences which are used up through the course of their lives. They are spiritually tied to a person - essentially a lifetimer. A person is unaware of their own essences as they are already created - not in the process of creation.
That is the fundamental weakness - the need to feed them with Life, which is difficult to attain legally, but can of course be sold, shortening a persons life span, in exchange for material wealth.
How are the essences/elements collided? Presumably the elements could be physically mixed, but what medium is used to transfer, say, Life? If it is something easily obtained (like blood) it could be possible for Homunculi to occur naturally.
For example, the Chosen One and his party are camping in the woods when they are ambushed by the Forces of Badness. During the scuffle, some blood is spilled on the campfire, mixing life with Fire and Wood. This could presumably also happen with animals. Homunculi created this way could actually survive in outside society by forcibly taking whatever transferred the Life they need to survive (vampires anyone?).
This leads to another question: do only humans contain Life? If not then every forest fire would spawn a thousand Homunculi as Wood, Fire and Life mixed. Also, butchers could sell bottles of Life along with sides of beef. Heck, farmers could live for centuries by harvesting Life along with the crops every year. The human lifespan would be expanded enormously.
If on the other hand only humans have Life, or Life must be give up freely, then all of the above is moot. But I think that there are a lot of cool possibilities if it is relatively easy to extract essences from non-human sources.
Combination of Fire/Fire/Spirit will create an "Elemental" as will any Duel-Element construct. These are invariably more powerful.
What distinguishes an elemental from the ordinary run of Homunculi apart from the sheer amount of power? Are they made entirely of their element? Also, by what standard are they more powerful? Do they have more brute strength in element manipulation, or can they accomplish more delicate tasks than any other Homunculus? Or both?
On a side note, how to you collide two of the same element? Bang two rocks together?
Last thing, have you thought of how these Homunculi are controlled? If their creator is their only source of life then simply withholding Life will work for more intelligent ones. But what about Homunculi with only dog-level intelligence? A doubt a Thaumigist has the time or the means to train an unruly Metal Elemental to obey his commands without some sort of magical coercion.
Hope I didn't come off as too negative, it's just that I have to ask questions like this when I find a magic system I like.