Easter Egger/cross for nicer roo
You ask difficult questions. First, the EE is already a cross. What that cross contains affects the genetics. Second, although personality traits can be inherited, sometimes you can get a great roo from a nasty one or a nasty one from a super nice roo. Have seen EE cross with all breeds of chickens. The resulting offspring are quite varied in looks, temperament, and egg laying ability.
If you want a sweet good tempered roo, then I would suggest that Salmon Faverolles are usually quite mellow. However, there is a possibility of getting a nasty one even in that calm breed.