This part about looking back in time is what interests me, and wondering what we will see. I'm having trouble comprehending this concept. Everything else will be gravy! Time to most of us is relative to a clock or calendar. Once it's operational, how will what it sees relate to us , here and now? I'm not really sure how to ask the question!!??
I will preface this by saying, to really understand this mathematically, you have to understand General Relativity pretty well, because the "expansion" we are talking about is space-time.
I presume that everyone understands the general concept of the speed of light, and that the further away something is, the longer the light took to get to you, so, further away = older. So, for example, when we get data from a Mars lander, that data was taken anything from 3 minutes to 22 minutes in the past when we receive it, depending on the distance. If it's very near us, not far, so not long, on the far side of the sun from us, it is a lot further away, so it takes much longer.
Same thing with this, the further away it is, the longer it takes the light to get here, so in effect we are looking at something from a long time ago.
The red-shift effect is where the analogy comes in. It's really a 4-dimensional problem, but the analogy is 3-dimensional. Suppose you have a spherical balloon, and are blowing it up slowly. Take a sharpie, and mark a dot on the surface - that's where we are. An inch away, mark another dot - a nearby object. Then mark a dot exactly the other side of the sphere from us - a distant object. As the balloon expands, the nearby object moves away from you, but pretty slow. The dot on the far side moves much faster away from you.
Blowing up the balloon, making it bigger and bigger, is analogous to the universe expanding. Of course, the universe does not fall on the surface of a big 3-dimensional sphere or bubble, it's a 4-dimensional sphere or bubble (but not uniform...).
A 4-d version of that is what the universe is doing - nearby objects move slowly away from you, and far-away objects move faster. The faster they go, the more the doppler shift they get, so, distant/fast moving objects have a lot of doppler shift, visible light toward the red, and then further, to the infrared, and ultimately towards radio wave. So something that looks like, say, a normal star from nearby, might only be seen as a radio source from a long distance.
This red-shift means that some of the visible light from the star (or galaxy, or supernova, or whatever) is shifted lower, beyond visible light, into the infrared. So to see it, you need a telescope that sees infrared. That's what this telescope does, it sees lower frequencies than visible light, therefore things with a lot of doppler shift, which means it is a long way away, which means the light travel time from that star is from *long ago*, effectively, looking at stars from the early universe.
The math of some of this is messy, but the idea is relatively simple.
Brett