As was explained in the introduction, "The Stream", or, Ambient Field is a near limitless source of energy that's constantly flowing throughout the entire Universe. The thing listed as the main source of The Stream's energy, The Casimir Vacuum State needs to be explained further, though it won't be fully explained here as it's not necessary, as well as overly confusing for most.
The Casimir Vacuum State is a field of energy in it's own right, caused by the Casimir Effect, where random pieces of matter and energy simply form and then annihilate themselves, releasing a massive amount of energy when they do, the total of all this energy then tallies up to about 10^113 Joules. To give you a comparison, across it's entire ten billion year lifetime of constant Nuclear Fusion, the Sun, the star at the center of our solar system, is estimated to output 1.2 x 10^44 Joules of energy. That's just over half of the energy that's passively contained, per cubic meter, within the Ambient Field.
Next, to further expand upon why the Ambient Field is also known as The Stream. It may or may not be notable by now (if not then it will be) how much a water analogy is used to explain and teach the mechanics of the Ambient Field, because it works like a river. While it is a truly massive amount of energy, it doesn't just sit there stagnantly. Partly due to things such as gravity and the movement of solar systems and galaxies dragging it around to form ripples of currents, and partly (on a smaller scale) due to our tampering with it and drawing from it, the Ambient Field moves and flows freely.
A notable pair of examples, are Ley-Lines (tracks and paths around the planet, through which magical energy flows faster, stronger, and is easier to manipulate), and Wells or Fountains (cities, counties, and sometimes even countries or Archipelagos where magic is stronger and easier to control).
To expand upon the list given at the end of the explanation to the second question, the "Mind", "Body" and "Soul" collectively are known as Tradiums. In almost all cases, these three things are needed to allow one to use magic, though while exceptions to these rules exist, such as Shadow Beings, Phantoms and Entities, (more on which will be explained later on), without one of them, it's either impossible, you're dead, or you're soon going to be.
Let's start here by defining, the "mind". According to the Oxford's English Dictionary, the mind (as a noun) is defined as "the faculty of consciousness and thought" or "a person's ability to think and reason", and for our purposes, that's exactly what it needs to be. The mind serves two uses when applied to magic:
1) It allows us to form a soul by giving us freewill (and in turn gives us true life).
2) The second use (arguably not as vital to life itself, but still entirely necessary for magic) is that the Human Mind allows us to control the energy our Bodies and Souls allow us to wield.
To expand upon this, Magic, and the massive amounts of raw power that can be put behind it, requires an incredible amount of mental ability to control. Even most supercomputers, with their ability to run trillions of calculations per second, have no where near the speed nor power to process and manipulate each and every individual string of energy used for magic. Computers think in straight lines, they work in grids, 1s and 0s.
The minds of living creatures however, to carry on with the shape analogy, think in circles and zig-zags, their thought process can bend and turn fluidly, which is needed to control a fluid force such as magic (not to mention, the minds of living creatures are millions of times more powerful than any computer yet developed, which is also needed to give the required level of control, even if most of this processing power is subconscious).
Secondly, we have the body. Once more, we will start with a definition, which is "the physical structure, including bones, flesh and organs of a person or animal". While the mind lets us control magic, and the soul is our source of power, the body serves as the intermediary, a conduit for this power. It is within the body that the mind and soul resides, and it is through the body that magic is channeled; when one goes to use magic, they must move to trigger it. Movement, is the easiest (but not the only) way of using magic, as it gives us a physical action to cause this magic to mimic, as well as a way for our mind to project magic in a way that's understandable to it.
A final thing must be said about the purpose of one's physical form in the process of magic. While the average Human mind is easily powerful enough to control high level magic with practice, the soul of the average Human isn't powerful enough to draw in the energy needed for all but the basic versions of the lowest forms of magic, such as hypnosis and illusions, which is where a Magi and the average Human differ in biology.
Magi possess a slightly altered immune system, which allows a form of genetic of semi-bacterial organism (Named Parvus Scintillae) to grow within their bodies. The PS Cells are unique throughout every Realm in the universe, as they act as a conductor of magical energy on a massive scale.
They evolved in an environment that had little to no ambient nutrients, and no where near enough warmth for them to stay active, to counter this, they adapted to draw energy in from The Stream, and convert it into nutrients and heat to allow them to stay active. This means that a colony of these cells, were able to draw in enough energy to convert it into matter, a feat which takes hundreds of thousands of Joules, even for the minute amount of nutrients needed for single celled organism. If these colonies are able to grow inside the Human body, then they act as the perfect conductor and amplifier for magic.
Finally, we come to the Soul. The Soul is an actual thing, an energetic mass that resides and permeates our entire body, in some cases it's even tangible in a fluid or, in the most extreme cases, solid form.
The Soul, is a collection of energetic particles known as "Ziel Particles", they are what cause the movement, the flow, of the Ambient Field: As they move, they pull the energy with them. This is why it allows us to connect to this near limitless pool of energy, as it draws energy into itself, to then be directed, though you could say that you're "redirecting the flow of the stream".
Ziel particles start to pool into the body of a creature during labor (or while it's waking up and forcing out of an Egg, for cold blooded creatures), they're attracted into the body due to the possibility for a sentient creature to change the course of what happens, or, in other terms, the Soul forms due to a creature having free will.
The Soul also serves one more purpose, the mechanics of which will be later explained. The Soul produces a sort of "heat haze", like the ripple in the air above a gas hob, this "heat haze", is called an Aura. Each person's Soul works on a different wavelength and frequency, which in turn changes the aspects and form of their Soul and Aura.
This is important, as the energy within the Ambient Field is considered "pure", by which we mean Neutral, perfectly centered in the spectrum. The Soul both draws this energy to allow us to use magic, but it also needs a supply of energy to hold itself together, else wise, it eventually burns though the energy within it, and disappears, so it needs the Ambient Field to carry on existing.
This, presents a problem, as if a Soul were to attempt to run on the pure energy from The Stream... It would be as if you were putting crude oil in a car, engine; it's not a good idea. This, is why the Aura is important; as energy flows into the soul, it first flows through the aura, which converts the energy from The Stream into the correct frequency and wavelength to match your soul, which allows the soul to process and use it.