Bekhorot 47: Who Need Redemption?

More on the human first-borns -- who is exempt from the need to redeem the first born. The son of a woman from the Tribe of Levi -- but if her husband a kohen or a levi, the child would already not need redemption. So is the father a Yisrael? A non-Jew? Also, would a kohen need to redeem himself? For example, a kohen who has set the kehunah apart from himself. And: a new mishnah! With the kind of first-born statuses for inheritance and for the kohen. Where a miscarriage is explicitly not considered to be a birth. What about a first-born who was delivered by C-section? And what if there is another child born via "natural childbirth" after the C-section? Some say that second child would also need to be redeemed.