As to your questions:

Dual Rates is a feature best left alone unless you fly 3D - More on that later.

Expo is short for Exponential. It is a way of "softening" the sticks near their center position. For example, without expo, when you give 1/4 stick, you get 1/4 servo movement - Likewise, 1/2 give you 1/2, 3/4 = 3/4 and full = full

With some Expo dialed in, (and these amounts will vary depending upon the percentage of Expo you're using) 1/4 stick may give you 1/8 servo movement. 1/2 will equal about 3/8, 3/4 =11/16 and full still equals full. So you still have full control, the sticks are just les sensitive near the center to help you keep your minor adjustments minor - Whereas, Dual Rates is a way of diminishing control across the entire range. So if you have your dual rates set to 50%, when you turn them on (with a switch on the Tx) at full stick, you only get 1/2 servo travel.

Before I go any further, let me explain what 3D is: This is a type of "Flying" where the plane really isn't flying at all. You need a very light plane with really big contol surfaces and a LOT of engine. In 3D, you are actually controlling the plane with the wing in a fully-stalled condition, so you can do things like Hover and other maneuvers that a plane shouldn't normally do.

So keep these huge control surfaces from being overly sensitive while you ARE flying normally, it's nice to have Dual Rates to calm things down.

The problem with using them on a regular plane is that many people forget to turn them on and off. I have seen countless crashed because someone tried to do a loop but forgot that their dual rates were on so they didn't have enough control to recover. It only takes one brain f@rt to total your plane.

Mixing has several purposes, but the two most common uses are to "mix" two controls together - for example, I have a Cessna 310 that needs a touch of down elevator when the flaps are deployed. So I "Mixed" 8% down elevator to my flap switch. Or you can slave two channels together so if you had two elevator servos, rather than use a Y cord, you could plug one into the elevator channel (let's say Channel 2) and the other into channel 5 and then make channel 5 slaved to channel 2 so that whatever channel 2 does, channel 5 will copy.