Eggs – What do I do with the egg that contains a crack while curing in brine

A few things aren't quite right here.

1- a cooler full of water for 3 days.
A turkey will take 3-4 days to thaw in the fridge- between 35-40F. Quicker methods call for submerging in running water for some hours. Submerging the turkey in stagnant water- even if it started as ice water- will allow the turkey to rise well above 40F over the course of 3 days. You would have to add ice or have the turkey somewhere colder than 40F for this to be safe.

2- brining too long turning a turkey to mush.
The salt in a brine denatures some proteins and supercharges the bird with water. These will make the meat more tender and seem more tender respectively. That said- the risk isn't that the meat will get mushy. Unless you are adding some other ingredient to the brine that is actually a proteinase like papain the risk is not mushiness but being too salty.

3- 1-2 days of brining.
I have never seen a recipe that called for brining this long. The brine recipes I have seen are on the order of 4-10 hours. If your brine recipe calls for this length of time then it is probably more dilute than the ones I use. In such a case it would probably be fine to thaw it in the brine if you address the safety concern.

The turkey being frozen will prevent the brine from penetrating but as the bird thaws from the outside in the outside of the bird will have more alone time with the brine than the deeper meat. I can't say whether this would be a problem- especially as Harold McGee says that the salt from brining isn't able to penetrate very far into the meat anyway.

Unless it is cold enough outside (or you have enough fridge space) that you could brine the turkey at <40F for 2 days while it thawed I would recommend at least mostly thawing it before introducing it to your brine.

I suspect that the biggest problem here is that your brine isn't anywhere close to being strong enough. Cooks Illustrated has a good guide to the entire process but in a nutshell:

• Sea salt is expensive and inefficient for brining; the impurities actually make it more difficult to dissolve and disperse properly. Kosher salt is generally recommended, although table salt is also fine.

• A typical brine is 1/4 cup table salt and 1/2 cup sugar per quart, which translates to about 70 g and 140 g respectively per L. For very high-heat methods (grilling/broiling), you halve the amounts. Also, for kosher salt you need to double the volume (no change if measuring by weight). Even the lower, high-heat cooking concentration is almost twice as concentrated as what you're doing.

• You also need to scale the amount of brine with the weight of the bird itself. The rule of thumb is 1 quart or L per pound (2.2 kg) of meat. For a whole chicken, which is generally around 6 or 7 pounds, 1.5 L of brine is nowhere near enough, especially if you're brining in a pot as opposed to a bag (does your 1.5 L even cover the chicken?).

• It doesn't really matter if you butcher the chicken first (although most people don't). You're exposing slightly more surface area that way but not really enough to matter.

• Make sure you are actually dissolving all the crystals! From what you're describing, you're getting high concentrations of salt in some areas and none in others. That means you didn't get proper dispersion. You really need to make sure that all of the salt (and sugar, if you're using any) is completely dissolved, otherwise you don't have a "brine", you have water with a bunch of little piles of salt. Some people will suggest heating or even boiling your brine to ensure proper dissolution; just make sure you let it cool off afterward if you do this, before submerging the bird.

In answer to your specific questions:

1. The container should be well-sealed to prevent evaporation, not to mention off-odours in your fridge. However, I've used pots with loose-fitting lids and had no problems. It doesn't make a huge difference as far as the efficacy of the brine.

2. Fridge temperature is ideal. Do not even think about using room-temperature water, that is highly unsafe for storing raw meat for 6-8 hours at a time.

3. As long as you don't overcrowd the vessel and do disperse the crystals properly, the actual amount of space is not a major issue. If it's exposed, it's exposed.

4. Longer than 12 hours is not recommended. Actually, according to CI, longer than 8 hours is not recommended. Don't overdo it - you're brining, not marinating.

5. No matter how you cook any piece of meat, it will give up a certain amount of water and therefore a certain amount of salt (from the brine). Left unstated is why you would even consider boiling a brined chicken; brining is primarily a technique for dry-heat cooking (roasting/grilling), and if you want to boil/poach/braise/whatever then you should be focusing more on flavouring the cooking liquid than the meat itself. I wouldn't bother brining if you're making chicken soup, there are better ways to flavour that.