Okay ladies, here goes. I had a hen go broody some years ago and her "due date" was Thanksgiving Day. Yes, late in the year, and very cold and wintery out that year, but she didn't care. I had tested the eggs and she had three viable eggs under her. Two hatched right on time and by Thanksgiving Eve she had two little peeps peeking out. The third egg was just starting to "pip" by Thanksgiving night.
However, 48 hours after she hears that first peep she leaves her nest, no matter who is left behind. That's just the way it is. There is a 2 day window from the first peep to her leaving the nest with the little ones even if there are lagging hatchlings behind.
So, the day after Thanksgiving we were heading out early to go shopping and I checked on the little ones, Mama Hen was out and about even though one egg was still rolling back and forth and you could hear the peep inside. I took that egg and I placed it in the little pocket my bra made, in the middle of you know what. Yup. We were shopping and the egg was moving around and you could hear peeping every now and then. It was able to stay warm all morning and by the time we had eaten lunch it was breaking through the shell. So we hurried home and I put the little guy on a towel in a box under a light and we all watched him come out.
I really think that he would not have made it, because she didn't return to the nest at all, she took her peeps back to the coop with the others that night. I snuck into the coop and tucked the little one under mom that night and the next morning she came out with her three little ones!!!
Anyway, as for using left over egg yolks, they do freeze, but they aren't quite the same when they thaw. It's best to stir in 1 tsp of sugar per egg yolk to help them be more fluid when they are thawed.
I many times use two egg yolks in place of one whole egg in yellow and chocolate cake recipes, just to use them up. Plus I have pound cake recipes that use egg yolks, custard is a favorite of my husband's.
And, yes, a fresh laid egg that is clean can sit in a cool place for several months. I had a few very dirty ones that I put in a bucket and I wanted them to rot so I could toss them around the garden as a deer deterrent. Well, it took 6 months before they were stinky! And I learned that deer may not like the smell but I ended up attracting both skunks and opossums with this practice, so I gave it up.
I regularly keep a dozen eggs on the counter and keep track of the date, after two or three weeks I hard boil them and they peel much more easily. My mother prefers hard boiled eggs with beets, so I age them for her. She can't keep them on the counter, if she sees them she thinks it's "wrong" and she has to put them in the fridge, so I do it for her. Go figure.
However, I only do this with the eggs that are clean to begin with, if they are dirty they get washed and in the fridge. If they are cracked they get used that day or cooked for the dogs.
Many people just call me the crazy chicken lady.