While skinks are in their natural habitat in the wild, they do eat raw meat. They are even known to be scavengers and eat meat that has gone rotten, that doesn't necessarily make it okay for them to eat in captivity.
In the wild blue tongue skinks can drop their tails as a defense mechanism against a predator that may be attempting to grab ahold of them, allowing the skink to escape to freedom.
Yes, you can offer your blue tongue skink eggs as a treat every once per month or so. However, eggs are very high in fat and cholesterol, which can contribute to obesity and other related health problems.