Why is psychopathy not even mentioned in the DSM? How does this affect the research and is it taken seriously in mainstream psychiatry? I understand ASPD is in the DSM, but it's not even nearly the same construct and has comorbidities atypical for psychopathy.

I don't know. It may be that it's felt to be redundant with ASPD; they're not nearly the same construct, yes, but there's still overlap and I seem to recall there being a paper in the Handbook largely concerned with factor analysis and that issue.

I was once told by a professor (medical biochemistry) about studies on empathy of health care professionals that used supposedly shocking pictures and some kind of autonomous response measurement. They had similarly suppressed responses as psychopaths. Have you come across such studies?

Not that one, no. The studies I recall being cited tended to be things like (failing to) match up words with emotional connotations in which the psychopaths did poorly.