"Pigments" are basically just loose shadows; they aren't pressed into pans. MAC's Pigments tend to be more color-intense than shadows, but not always. Pigments can be used dry, or layered over a cream shadow to encourage the pigments to stick, or mixed with something to create a more creamy effect (MAC makes some available on the Pro site, or some people mix with glycerin or Visine or other products- do a board search for more info).
Also, many pigments can be used on other body parts - to create shimmer on the collarbone or shoulders, to dust a bit into the hair for a cool night look, to mix into nail polish, to create a new lip gloss. Millions of uses- just do a board search for ideas. Not all pigments are color-safe for other areas like the lips, so search the safety posts for more info on that.
You can use a variety of brushes- some people use their fingers! I use the same sort of brushes I use with pressed shadows, varying them according to the look/technique I want. For example, for concentrated color I use a flat, stiff brush and pat the product onto the lid. For a lighter, softer look I use a fluffier brush and dust it on.
Loose pigments can be messy, so you may want to do your eyes first, then clean up before doing your face!
As for greens, you can always try a less expensive brand first to see if you like greens on you, but remember that those lines don't carry the same color impact that MAC, Urban Decay and other brands do. Why don't you go to Sephora or to MAC and see if an artist can try some greens on you? That way you get a good suggestion as to whether to use cool blue-greens or warm olives.
HTH.