Mixes are used simply because no airplane is perfectly symmetrical and all airplanes (no matter what the designer tells you) have some form of of coupling. For example, let's say your elevator isn't perfectly centered. Whenever you deflect the elevator, you're going to apply uneven forces to the left and right side of the plane and it's going to want to roll. A good builder can minimize these effects by meticulous building, but it can never be completely eliminated. Other coupling effects stem for the basic design of the plane. For example, the rudder may not have an equal surface area above the center line compared to below the center line. This is going to create a tendency to roll when you apply rudder. And the list goes on.
So, in its most basic form, mixing can be used to eliminate these tendencies. For example, if your plane wants to roll left when you apply hard up elevator, you can mix in a couple of percent of right aileron to compensate for that. The result is a plane that flies truly perfect with no coupling. It's not easy to get it perfect (in fact, I'm still learning) and requires some practice and trial and error.
Which surfaces are mixed together? The answer is "any surface" and sometimes even the throttle. In the example above, we mixed elevator to aileron. Let's say your plane wants to pull towards the canopy when you're flying KE and applying a fair amount of rudder to keep it flying. In that case you can mix in some down elevator with the rudder to compensate for that.
And that brings is to the mixes that are controlled by switches. Let's say you want that rudder to elevator mix when you're flying KE, but you don't like how it affects upright flight. Well, then you can (on most radios) assign the mix to a button, so you can enable it when you're in KE and disable it otherwise.
So do you need mixes on your airplane? Well, do a couple of loops, turns and KE passes and check if you're completely free of coupling. If you are, you're truly lucky, but chances are that you have at least some of it. Figure out what axes overlap (e.g. pitch and roll) and dial in a mix that compensates for it.