I have "ice packs" which are encased in plastic (some hard, some soft), that I keep frozen. It won't quite bring your soup down as far as you want, but dropping a few of these into your soup will help cool it off. Just remember to clean them before returning them to the freezer.
The other thing I do it put the stopper in my sink and add cold water and ice. The whole pot goes in the sink--surrounded by cold water and ice it will cool much faster than in the fridge (or freezer). Add some salt to the ice-water and it will get even colder. Stir it up a bit every once in a while both inside and outside (use separate spoons!) to keep the temperature distribution even.
Alternatively, you could use one of these :)
There's not really much chemistry happening here. It's just basic physics - ice crystals form when you freeze it, tearing through things a bit, and then they melt back into water when you thaw it. Some proteins are indeed sensitive to denaturing during freezing, but that's basically going to be a constant no matter how you freeze it. (Denaturing is just a destruction of the tertiary structure of the protein - so it will mess with its structural properties, but since it doesn't destroy the amino acids, it won't alter nutritional value. I don't know if structure-giving proteins in meat are sensitive to freezing denaturation, but I don't think there's anything you can do to affect it anyway.)
With respect to your first question: it's not the ice formation on the surface that matters. That's just sitting on the surface. It's the ice forming in the chicken that's tearing it apart. Amount of surface ice doesn't have an effect on the food underneath. It does mean that there'll be more water when you thaw it, though, and sometimes that's very undesirable (e.g. for bread) and sometimes it's just annoying (vegetables that you want to cook without much water). But all that matters for the food itself is the fact that it's frozen. This is the same kind of the thing that you see with fruit - if you freeze and thaw it, it'll be completely mushy, now that the ice crystals have destroyed its internal structure. This isn't so pronounced with meat, since it doesn't have as high a water content, but the texture is still somewhat altered.
For your second question: it's just a matter of how much moisture-containing air was able to get to the food. This is a common problem. The ideal case is a completely vacuum-sealed, airtight container: only the food will freeze, and there's no room for moisture to get to it and form surface ice. If something is airtight but was sealed in with normal, somewhat humid air, that moisture will create frost on the food. If it's not airtight, air will leak in, and humidity is brought in when you open the freezer, so it'll slowly accumulate frost.
For your third question: once something is frozen, it's frozen. It's not moving anymore. Pores aren't being opened. There's no effect from food being frozen longer. (Unless it's not airtight, in which case it can take on odors from the freezer - but that takes a while.)
I can think of two things which could conceivably have an effect: freezing at different rates, and freezing and thawing multiple times. The former is hard to mess with at home, but freezing very rapidly reduces the amount of destruction. In a home freezer you're already freezing very slowly; freezing more slowly probably wouldn't be significantly different. Multiple freeze/thaws should tear things up a bit more (though probably two freezes won't tear things up twice as much, since some crystals will just form in the same place they did last time).
Best Answer
I have not tried this method myself, but it sounds reasonable.
It involves filling a clean milk carton or juice container with water, freezing it and then bashing it against a wall to crush the ice. I guess the container has to be quite sturdy to take the beating without breaking. Could be worth a try.