Starting traits will be above any other traits affecting the same thing. If you take psychopath, you will lose no mood when killing humanoids right from the start and evil traits will therefore do nothing. However, later evil traits will start actualy giving you mood for killing humanoids, but you will get nothing because you have the psychopath trait. I think this will balance things nicely since you will benefit from these traits at the start, but they might prove to be less useful later on as you get more morality perks. I will also add a proper way to change your traits mid game so you are not stuck with traits you don't like forever.
As for bonuses like more money from working or sale discount, these will simpy stack with other traits.
The evil icon is a mix of both generic devil and things in the game.