So alot of the tutorials already been said and pretty much applies to what all the questions say. Ill try to address the questions directly for something different.

But when should a shadow be blue, or purple?
It really depends on a piece for the color. But in order to determine a shadow in the first place, its pretty much what Vineris and Cnids has, determine the light source to determine the shadow. Its always values intertwined the color. For the color reason, it really depends on the mood, and what look your going for. A nice tint I like to use for my darkest values (usually found underneath something), is a mix of brown and blue. It will give it a nice blue tone, but it also saying that nothing in the real world is truely black.

As you see the purple kecleon, the colors scheme can be primaries, and so the shadows are brown and blue. The reflected light is a bit purple, because the light from the ground is a bit blue and the red of the kecleon is mixing a bit with the blue. So it also depends on what color light is bounching off the object too.

How do you incorporate mood, but keep it realistic?
Im not sure what you mean, because It not only depends on how you define mood, but also realistic. There is alot moods that can be real or not. Carvaggio, uses the opposite of the Renaissance people like really ugly colors, and the most eerie of moods. He use peasant people for models. Extreme lighting, and gestures, can set off a mood. Extreme light/ gestures though was also of the Renaissance. When I mean gestures, I mean that all the figures seem to suggest something, like pointing at something, open hands, a wide gazes or in other words, a good storytelling with good emotions of the figures.

Maybe its the strokes in your pieces. Although you won't see them often because usually more strokes can create a lesser realitstic piece, strokes can create a psychological mood. Expressionism is a good example, and especially Van Gough.
[link]

Mood really encompasses in almost any elements of art. However if your saying if you want to make color to define mood, then start like word playing with what color you want to do. Its almost like any other art piece is to brainstorm. It usually should start after a pencil sketch. On that thumbnail piece, you can just plann out your colors. A good way to think of your color pieces is to do word playing. A good tutorial is this one:
Or you can gather inspiration. One thing is that you can take colors from a real life setting in a photo. Concept artist usually do this, to make a natural piece, where they take a photo and color pick it. Or you can also just look at art pieces and see what they have done.

Or also, it helps to paint in a solid color first in the background. You can then play around with it later. It helps to set a mood and helps pop out a piece, instead of staring at a white piece of paper.

When do you saturate colors and when do you desaturate them?
As a general rule, its all about contrast in your piece. The more saturation, the more the piece appears to come forward. The less Saturated, the more it recedes in the background. The most saturated colors, should receive the most attention, so it should be the center of your subject matter, and the less saturated help you focus on the subject that should receive the most attention. But, there isn't exact science, and it really depends on the piece. You just got to play around.

Also, my backgrounds are just hideous. I'm to figure out what's the best way to paint them. Using brushes, or just speedpainting.
Backgrounds still encompasses every element which piles into composition. Therefore it shouldn't be treated separately, it should be thought from the beginning. It is a matter of perspective, but it really depends on what your painting. The background should be part of the piece, and helping the mood, but should never be the focus of the piece. You want to draw the attention to the subject.

I would recommend also reading fox-orian's tutorials. Its pretty much everything you need to know, with all the elements of how to paint. I feel that not all the elements will be used, so you just got to think and experiment with the knowledge of each elements.

is a very good reference on lighting and colour.

The problem is that you're looking for a couple pages' worth of tutorial to explain how to draw an entire world. How is that going to work? What tutorial is going to tell you how to draw everything in easily-digestible sentences, and if such a thing existed why wouldn't we all be brilliant art geniuses?

Colours are really about understanding light. Environments are about understanding perspective, light and form. While it's nice to keep colour schemes in mind, simplistic solutions will always result in simplistic, naive pictures. If you want to do better it's time to stop relying on formulas, stop guessing and hoping you accidentally hit the right colour, and go look at it. If you're doing an environment you can't go to, look at good photos.

This will help you get started with light: [link] but it's not a substitute for looking at lighting effects yourself. The world is a cool place. You seem to like drawing forests. Take every opportunity to get outside and be in one. While you're out there take some pencil crayons or watercolours and start recording what you see.