Cells frozen in science all have different protocols depending on the type of cell and it's intended future use. Bacterial cells like E coli kept for the long term are stored in glycerol stocks at pre determined concentrations at -80C for optimal restoration when put back into culture, but sometimes are flash frozen in a media at a certain growth stage to be "competent" as in to have the ability to pick up plasmids if one so desired. These are generally flash frozen in liquid nitrogen and thawed on ice for use. Eukaryotic cells, like stem cells, cell lines, and primary cells are stored in liquid nitrogen at their pre defined concentrations in pre defined media, and are slow frozen and quick thawed for restoration. As with either method, they do get old and many cells do die in the process the longer you keep them even at ideal conditions. At this time, you can't really save things "forever" and even cell lines can undergo a thing called "drift" where the cells can change and no longer have their original founding characteristics.
The eggs from the chickens you want to hatch will store for different periods of time depending on the environment they are kept in for storage. Ideal temps and humidity can have the egg last a month and still get a few to hatch. The rate of deformities and thus quitters greatly increases as a function of storage conditions. If it is really cold or hot (or any deviation from ideal), the ability for the cells in the blastocyst of the egg to properly develop declines. Nutrients for the chick break down, natural enzymes in the egg start to degrade themselves or each other/components, the DNA/RNA quality decreases, the replication machinery starts to "go bad"....
To answer you storage question, in the lab where I used to use chicken eggs, 14 deg C (about 58F) and near 100% relative humidity was our ideal storage temps for the best and most consistent development of stored chicken eggs.
Of course, anyone who really knows this stuff will find this explanation rather sloppy, but the idea is there. It's late and I'm procrastiating. LOL Back to work I go!