I don't consider myself an expert, but as a farm kid and a sailor I know how to keep eggs! So I'll share what I do
If they are clean, and I mean spotless, they go into a basket on the counter where it is cool all the time (65 degrees or less)
If they are dirty, a little, I wipe them off dry and go into a second basket on the counter (to be eaten soonest)
If really dirty (which I haven't had since keeping the roos locked up separate - they were stepping on them) I wash them off and go in the refrig. since I have quite a few, these get fed to the puppies as a nutrition boost since they are growing so fast.
refrigerators are too cold for most eggs, although they will last for months in there.
To keep long term without refrigeration you can soak them in solution of 1 part bleach to 10 parts water for 20 minutes, allow to air dry thouroughly then handle only with sterile gloves or meticulously washed hands packed into sawdust or sodium silicate and stored in cool dry dark area
eggs can also be frozen (without the shell) I use a freezer bag and used for baking.
If you have ANY doubts, float test the egg in water, if it floats or even bobs chuk it...
You can also hard boil the egg, I like to leave the shell on till I'm ready to use it
Hope that was helpful, eggs last (surprizingly) for a really long time in the right condition, the store bought kind are usually already months old by the time you get them, what spoils them is the bacteria growing on the shell that eventually works into the egg that's why they are refrigerated, to slow the growth of bacteria, and has an ideal place to live and multiply, the gas produced by these bacteria makes them float in water. Washing an egg removes the protective film on the egg and helps bacteria enter - so I don't wash my eggs.