Child/adolescent/adult is conditioned by an admixture of experience and genetics to relate to others in a way that is indifferent, or outright adversarial. This may be with exception to select groups or people. That is the theory behind what "AsPD" is.
"What would you say the core traits of AsPD are that most, if not all, people with AsPD are likely to have?"
AsPD being a clinical term, and diagnosis of it resulting from psychological evaluation, they'd probably lack empathy and have an whatever mixture of criminal traits. Most are diagnosed when they have to see a psychologist, and they often end up in the doctor's office because they've been compelled to, as a result of misconduct. All persons with "AsPD" will have a "lack of empathy for others and lack of remorse about harming others," as that in itself is the core psychological component of said personality disorder. I believe that also answers your second question.
"If you don't have AsPD, but know someone who does, what do you think their most predominant trait is?"
I know someone who exhibits all of those behaviors rather dramatically. He doesn't really "feel superior." That's the only thing that doesn't match.