a) Yes, an annulment is required. b) baptism is not required for a valid marriage.
Baptized person, divorced from non-baptized person, wants to marry Catholic. Annulment still required? Or does the Church still recognize this marriage?
No, but paperwork must be sent to Rome for dissolution of the marriage. See "Petrine privilege" in my post above.
(lol, no, I'm not planning on marrying very soon, but it's good to know nonetheless)