I have heard about using the mineral oil and keeping the eggs in a cool, dark place and they should last about 9 months. But I have not done it as I can’t find a place that sells fresh eggs around here. I do pickle eggs but yes you need to keep those in the fridge.
One way to tell if an egg is bad is to put the raw egg into a pan full of water. If the egg stays on bottom on it’s side it is good. If it stays on bottom but up on end it is still good. If it floats to the top it is no good and you need to throw it out. Hope this helps.