Anything you feed your rat that comes from an animal should be cooked thoroughly. Do not give them raw meat or eggs.
Egg is okay for rats, but I would not give a rat a full egg to itself. If you want to give them some, I would advise cutting small cooked chunks and feeding a little as a treat, or putting it in with their mix. A full egg is way too much for one rat, a quarter of an egg would be quite sufficient for a once-a-week snack.
I am guilty of feeding my rats little bits of egg from my breakfast every other morning, but they get between 3-7 hours of free-range exercise a day, sometimes more.