Question: How can Lizzie's father have died in the fire when in an earlier season, Red killed him in the hospital when Lizzie was already an adult?
Question: Over several episodes we see Captain Holt in competition with other Captains for the position of Commissioner. However, we have seen several Deputy Commissioners on the show. Is Commissioner a position that only Captains are eligible for? Are Deputy Commissioners ineligible? How realistic is this?
Answer: In reality, the Commissioner is a civilian administrator, appointed by the mayor of New York City. He (as of this writing, the role has always been filled by a man; the show gets that part right) is usually someone who has risen through the ranks of the NYPD, but upon becoming Commissioner, is no longer a sworn member of the force (the highest sworn rank is that of Chief). Since Commissioners are appointed, technically anyone can serve in the position, including Deputy Commissioners (who are appointed, in turn, by the Commissioner himself).
Update: On 1 January 2022, Keechant Sewell became the first ever female commissioner of the NYPD.
Answer: The man Red killed, Sam Scott, was Lizzie's adoptive father, not her biological one. However, at that time Lizzie (and thus the audience), was led to believe her real father abandoned her and her mother, so expect more secrets to be revealed how her real father actually died (or if he's even actually dead).
Bishop73