Argentine black and whites have a reputation for being more commonly docile. I've had a number of Columbian black and whites that were defensive and standoffish. But as with any reptile, there's no temperament that's species specific, they are individuals like dogs/cats/humans.

The cooked eggs and raw meat is a fallacy, I don't know where it originated. Whole food items only are suggested. There are a lot of people feeding that stuff, but what you "can get by with" and what you "should do" are two different ballparks.

Tegus are also different in that their diet has a fruit/vegetable component in it. They are omnivorous. Do some searches on that and you will find they have a more varied diet than other reptiles.

You are correct in your enclosure assumptions, mainly because Tegu require a high level of humidity that you cannot achieve without having a custom enclosed cage with moisture retaining substrate. Screen tops/sides will be detrimental and you will never be able to achieve the temperature/humidity gradient you're looking for.