We actually just had an issue with our fridge freezing all of our eggs because they were in the back of the fridge.
I move them to a different location and they were no longer frozen, we used them for cooking and they cooked just the same. No one had any complaints about them and they said they didn't even notice a difference.
Usually if I have frozen eggs from outside I will scramble them for the dogs or for the chickens.
I'm not sure how you would test if they were frozen, but I assume you could take a flashlight and candle the egg to see if there is movement inside of the egg from the yolk. If there is no movement, the egg would be frozen.