I apologize for the delay. But no, the second sentence is not correct. You may say:
What kind of person is he? ans. A responsible and courteous person
You might even use the singular if you point to contradictory traits:
What kind of person is he? He is a kind, as well as petulant, person.
However, we wouldn't refer to an individual as you have written:
"What kinds of person..." Perhaps this is because, for all a person's contradictory traits, he has only one character.
"His character can be seen to be comprised of many different traits."
You wouldn't say his "characters," and you would say "kinds of person."