Yes, it is fine to feed cats cooked eggs. Cats in the wild often eat both birds and their eggs. Just be careful about raw eggs due to the disease risk.
No. Eggs contain an enzyme called avidin. It decreases the absorption of biotin. It can further cause coat and skin problems in cats. You should stick to regular cat food.
Yes, it is safe, and many people do feed eggs to their cats as a healthy protein. Some people prefer not to give the yolk to their pets because yolks contain more cholesterol and phosphorous. It is important to cook the egg whites until they are hard.
I see no reason why not to. Of course, not too many, cause cats are small animals, so they should eat an egg or two, not more. Eggs are fool of proteins, and cats need them too.
