*gets the crazy eyes*
Gwyvian. @w@ We need to talk.
Given the hints we have about the fractal nature of the DA universe and the (very theoretical) relationship between OGSes, Gods, and the brilliantly-burning souls we know of as "stars" as functional aspects of a single, once-unified mind, the potential for the Big Bang / Big Crunch of the universe as a scientific parallel for the process of Jungian individuation has driving me insane for a while now, but psychoanalysis is very much not my field.
I can point out how the emergence of Pantheon and their various domains map to the brain and throw some hard science at DA's primordial creation myths that suggest the gods and other sentient entities of Thedas are a single mind taking itself apart and putting itself back together, but aside from an incredibly shallow understanding of the basic concepts of Jungian analysis, that's it. That's as far as I can go.
Gaider has more or less built this world on a Jungian model: the sleeping Fade of the individual being the personal unconscious, the raw Fade being the collective, populated by spirits and demons (literally "daemons", neurologically) acting independently for the benefit and detriment of the conscious mind that is the physical world, etc, etc. But I can't dig any deeper than that, and it feels like something pretty fundamental has to be underlying the whole thing.
I would absolutely kill for a beginner-level description of exactly how individuation works. (Not intended by the writers I'm sure, but it's kind of hilarious that Thedas is in its Middle Ages... hee.) Also, does Jung get into things like repression? The effect of pushing things down into the subconscious- that sort of thing?
I am at utterly your disposal to talk about this subject! *bow*
This is actually quite a good understanding of the parallels, the only thing I would add is the respective relationships of these various layers. As I said in my alchemy post, Jungian psychology has a heavy basis in the magnum opus among other things; not to digress, the short of the construct is: the persona, the ego, the shadow, the animus/anima and the self.
Because this relates to your question, I shall start with the shadow: there is indeed repression in Jungian psychology, albeit the Jungian model is based on a slightly different construct than the traditional definition of repression you might find in Freudian psychology. I.e. repression is already accounted for in the whole unconscious/conscious divide, meaning that the shadow realm (the personal unconscious) is where the base instincts of people is pushed down into. The shadow is quite an important part of this model, because Jung recognizes the fact that one is simply not a complete person without this aspect of him/herself, yet he also recognizes that in order to function in society, the persona (i.e. the face we show to society) is a requirement. Many basic problems come from an extreme reaction to this balance in either direction: the desire to see the destruction of the persona or the desire to utterly quash the shadow. The shadow is where projections come from, too: an unconscious reaction to elements we instinctively know belong to our darker side, e.g. we loathe someone without any good reason (this is a recognition of something in ourselves), or complexes which cause us to see things in our surroundings which aren't actually there, e.g. we perceive someone to be brooding when in actuality they are fine. In general, Jung places a great deal of importance on dreams and visions, which all connect to both the personal unconscious and the collective unconscious, i.e. in Thedas, as you rightly say, the sleeping Fade and the raw Fade.
According to Jung, it is a mistake to assume that people "grow out of" the kind of "inferior" behavior that society requires us to repress throughout the developmental process, i.e. when one is an adult, aggression, lust, etc. that is left to run wild in early stages of development have not vanished at all, they are merely kept in check, so to speak, and when people do unexpected things (i.e. they snap and kill someone or they do something you would never think they could do), that is actually an expression of the shadow. It is also true that there is something inherently unnatural in someone who is so attached to the persona that they seem flawless and it leads to a shadow being cast anyway, because one cannot light a candle without casting a shadow; people usually sense that there is something horrible and dark in such a person. Which is actually true, though perhaps not as dramatically as one might assume, seeing as everyone has a shadow and that does not mean that they are inherently evil; it is all a matter of balance and whether or not one tends to both sides of him/herself. I find this part particularly fascinating, as people have such a knee-jerk reaction to their shadows, yet they are increasingly ruled by them the more they try to suppress it. It all makes sense to me!
The animus/anima is the realm that represents the opposite gender in the psyche, i.e. anima for men, animus for women; to put it very succinctly, you could say that this is the "mold" by which we choose our partners, the repressed elements of gender which is not ascribed to us by society... and I could go on, but here all I have to add that is even mildly on-topic is again the creation mythology: where male and female become distinct in terms of Mother Earth and Father Sky, the first division where such distinction matters and upon which the balance of duality is founded. That's universal enough that it would be a horrible oversight to leave it out of any self-respecting mythopoeic world.
The persona I touched upon already; all I would add is that this is the very surface, what people seem to be, and it is at the core of society in general. It is the foundation upon which all "othering" or differentiation creates conflict, which is again inherent to any self-respecting mythopoeic world, because it has such a strong anchor in our world. The important thing is that it is the persona model which adheres to the ideal of everyone in their place and everyone doing what they are good at; in its purest form, this would be the Qun. You cannot be a cobbler and a poet at the same time, it says, even though the true person behind the persona is much more complex than that.
The ego: this is possibly the most important and volatile of the layers of the psyche, as thought, emotion, sensation, intuition all revolve around the ego. The ego is inherently selfish, yet it is the ego that enables us to function normally, as to be able to be individuals; you must be able to distinguish yourself from everyone else. In this, I would say that here there are few large-scale parallels to be drawn apart from these obvious categories; we have elements of thought, emotion, etc. which are symbolized in many, many things across Thedas (not the least of which again involve demons and spirits, as you pointed out, all suspiciously named after virtues and vices that poke around in our mind).
I'm trying to be as succinct as possible, but it's a large subject. 
A beginner's level description of individuation... I think I can do that: imagine a tree in soil. The soil is the collective unconscious and the roots are the personal unconscious. In the trunk you go through the layers of the superego from within to without; the inner core is the true self, followed by the animus/anima, then the shadow, then the ego and finally, the persona, which is the outer bark. Growing from the collective unconscious upward, the crown of the tree becomes the final product of individuation, drawing on the roots of the collective/personal unconscious, filtered through the various layers of the psyche and finally reaching a point where the tree is truly an "individual," i.e. a fulfillment of the collective qualities of humanity by coming to a point of self-realization. (Much like the Big Bang/Big Crunch idea: you grow outward to finally reach the innermost point of your being, purified into an individual born of a collective, who then contributes to the collective which will bear more individuals.)
This is not to be confused with Western culture's idealized "individualism," which ultimately promotes selfishness and disregard for fellow human beings, of course. In fact, individuation can be seen as quite the opposite: the ego, while fundamental, must be put aside in order to fully transcend this process of growth. You become part of a whole, an individual with a healthy psyche who functions as a "representative" of the collective, in a sense. One may think that this is already described in the persona, yet this is also not true, as the persona is something that is dictated from the outside-in, not inside-out; the persona requires a restriction of your true self and a rigid adherence to what is expected of you, while individuation requires the ability to deviate from the norm without being consumed by the shadow. (The qunari would hate Jung.) In essence, individuation is the point where you become a fully developed expression of the collective, which you chisel throughout your life.
I would say that individuation is actually the most significant part of mythopoesis in general, because this is essentially what is described as the "hero archetype;" in mythology, the hero is the bridge between mortals and gods, the process of becoming someone unique and productive to society by embracing their inner godly powers and distinguishing themselves from other mortals by becoming the best they can (and I'm really barely scratching the surface with that). This is what is attributed to the adolescent phase of development. Now, as a mythopoeic form of art, any fantasy requires that there be some sort of hero to act as a role model for the reader/experiencer, which in DA is the Warden, Hawke and the Inquisitor, respectively. Individuation is what gaming is all about in a sense, but RPG's especially so, as they conduct actual mythopoesis.
...aaaand I will stop now before someone throws something at me.
I might as well just paste my thesis in here at some point and that would summarize all my thoughts on this latter subject, but I shan't torment everyone with that.
Back to theory-crafting! 