How to make large clear ice cubes

Freezer burn occurs when water molecules in food gather in a colder location in your freezer—whether that be the sides of your freezer or even other foods.

Tips to prevent freezer burn:

• Don't put hot food directly into your freezer, let it cool first
• Put your food in air-tight containers
• The longer food is in the freezer the greater your chance of freezer burn

I'm going to go out on a limb though and guess that—at least with your ice cubes may just be acquiring a "freezer smell" from the other foods in your freezer. If I don't use the cubes in my freezer fast enough they end up tasting really unpleasant. Give your freezer a good cleaning and cover your ice cubes with saran wrap and this should help stop the funny smells/tastes.

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).