Leviticus 12:1 to 13:59, Second Kings 4:42 to 5:19
Verse 12:5 refers to verses 15:19-24. Apparently at least parts of these chapters were recorded in a different order than they were originally related.
In verse 13:2 the Torah does not say, as usual, "God spoke to Moshe, and said, 'Speak to the Children of Israel...'" Why not? R'Bechaye answers that God does not want his name mentioned in connection with bad things, for God does not desire our harm (Ezekiel 18:23); God wants us to increase in righteousness and Torah (Isaiah 42:21). Similarly:
Genesis 1:5—God's name is mentioned with the creation of light
Genesis 1:5—God's name is not mentioned with the creation of darkness
Genesis 1:28—God's name is mentioned with his blessing on Adam and Chavah
Genesis 3:16-17—God's name is not mentioned when he curses Adam and Chavah
Nevertheless, God's name does appear with three bad events: when he curses the snake in Genesis 3:14, when he curses people who break the covenant in Jeremiah 11:3, and when he curses someone who relies on people instead of God in Jeremiah 17:5.
Infants are not born in a ritually unclean state. The mother becomes ritually unclenan because she is "incomplete" due to the loss of blood. In time, she replaces this lost blood and becomes whole again. The ancient rabbis had varying opinions about why a woman who bore a daughter took more time to become whole: some believed that more blood was lost giving birth to a daughter; others believed that the mother "lost more" by producing a child that would not continue the family's lineage; others believed that the mother "lost more" by "sharing" with the daughter the power to have children.
Tradition teaches that a woman brings a chattat (atonement for sin) offering after giving birth because all women in labor make rash vows. ("I'll never be willing to do this again!", etc.)