Brine
Some assorted thoughts, before I try to guess an actual quantity:
Dependence on overrun shouldn't really be significant, as long as you're mixing well. The air doesn't add significant heat capacity, but it will make heat transfer less effective by providing some insulation, so you do need to mix well.
I can't imagine dependence on type of ice cream being that huge - whether you're using cream or egg yolks, you've still got plenty of water. I found a table for specific heats; it looks like eggs have a slightly lower heat capacity above freezing, and slightly higher after. I'm not sure about just the yolks, or about the latent heats of either. In any case, the properties of the ice cream custard will be somewhere between water and those. (Wildly generalizing, ice cream might be 1/5 sugar and 1/6 fat by weight.)
The more salt you have in your brine, the colder you can get it before it freezes. You won't be able to get it as cold if you don't have as much salt. I think you were slightly misinformed in chat: 0F (-17.7C) was defined (for whatever reason) using ammonium chloride. Saltwater brine (sodium chloride) can reach -21.1C (-6.0F) with 23.3% salt by weight (source: wikipedia). I believe the freezing point is roughly linear as a function of salt concentration; in any case, it'll be the most effective with the highest concentration.
You missed one factor that may well be bigger than anything you listed: heat coming in from the environment. This will depend on how well insulated your outside vessel is, the ambient temperature, and how much surface of the brine is exposed. (Also on how much you're gripping it with your hands, I suppose.)
As for quantities, I could try to ballpark something using specific heat/latent heat, but I think a far better method is to just look at the recipes for "ice cream in a bag" - the general idea of those is to put the ice cream mixture in a smaller plastic bag bag, inside a gallon bag full of icy brine, and shake. There are a lot of recipes using a sandwich or quart bag with 1/2 to 1 cup volume (probably ~120-240g) ice cream mixture, inside a gallon bag with at least 2-3 cups of crushed ice plus plenty of salt (maybe 300-600g? hard to say). I also found this one with the brine just in a bowl, using a pint (probably ~475g) of ice cream mixture and 3-4 pounds of ice. The latter is a little easier to estimate based on; it suggests for 100g of ice cream mixture you might need 300-350g of brine. (The other recipes are consistent with this.)
Mixing
This is really a separate question from all the brine stuff. If you want to get good ice cream, you absolutely must mix (churn). This both helps minimize crystal size and incorporate air. (Unlike whipping a liquid, mixing during freezing doesn't have to be as vigorous to get the air in.) It's possible that if you freeze it fast enough, you could make up for the air part with your pre-whipping, but I suspect you'll lose a bit of that volume during freezing. So at the very least, stirring will break up crystals, and it may well give you airier, fluffier ice cream too. (I'd be careful with that New York Times recipe I linked to; it's going to be prone to giving you unwanted crystallization if you don't take care with the "kneading", and may not leave a lot of overrun.)
General advice
I know you may have reasons not to do this, but in general, if you're willing to go to this much effort, you might as well buy an ice cream machine if you can. The part that you freeze will probably take up less freezer space than the ice/brine you'd otherwise use, and it'll also do the churning for you.
An answer to your edited points.
Number 4. Pores don't do much during cooking. It is about cell walls and proteins. A pore is a channel constructed from zillions of cells (like a tunnel constructed from bricks). A cell is like a bubble (the cell wall) filled with liquid (the cell plasma). The cell wall is made from zillions of proteins, like a hat knitted from wool. In freezing, the plasma turns to sharp ice crystals and tears the cell walls apart (like poking holes in a hat).
Then under heat, the proteins unravel the way you could unravel a knitted hat if you tugged at it. If you cook the meat just a little, the proteins remain bushy and soak up liquid. If you overcook it, they stretch and start looking like a long, smooth thread and can't soak up water and/or cell plasma any more. The meat tastes dry and unpleasant.
Freezing the meat is just bursting the cell walls. Unravelling the proteins is denaturation. They are two different things.
Number 1. More water does indeed mean more damage to the cell walls. No denaturation happens there, as explained above. But you can't change the amount of water within the chicken cells in any way while it lives. This amount self-regulates, like blood pressure. If you feed the chicken more water, it will excrete more water, not store it in its cells.
Number 2. You want lots of air around the chicken if you want to get ice crystals buildup on its surface. That's why Sobachatina suggested an inflated bag - to keep air around it. Also, unpacked chicken will make your freezer dirty and contaminate other food with uncooked meat juices, which is dangerous.
Number 3. As far as I know, water ice expands while cooling from 0 to -4°C and then starts shrinking. Most damage is done while the crystals expand, so I suppose that most of the damage will be completed within the first 1-2 days (depending on how long it takes for the complete chicken to cool to -4°C).
Best Answer
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).