Apparently Paul and members of the church in Corinth corresponded by letters. None of the letters from the Corinthians to Paul have survived. All that remains of their correspondence are in 1 and 2 Corinthians.
If an unbelieving spouse leaves, let them leave. It's okay to divorce them. (7:15)
This is the basis of the "Pauline privilege" in Roman Catholic canon law, which deals with a marriage between two unbaptized persons, in which one party subsequently converts and is baptized. (The "Petrine privilege" is similar, but refers to a marriage between baptized and non-baptized marriage partners.)
Our ancestors sat down to eat and drink, and then rose up to play (10:7)
Paul is referring to Exodus 32:6 here, where God and Moses tell the people to kill their family and friends for worshiping Aaron's golden calf. (Episode 39)
This refers to the plague that God sent on the Israelites for having sex with the daughters of Moab. God stopped killing people after Phinehas impaled a couple while they were having sex. According to the story in Numbers 25, God killed 24,000 people in the plague, but Paul corrects the number by saying it was only 23,000. (DWB: Phinehas's double murder: A killing to end God's killing, Episode 66)
Don't tempt Christ, as some of them did, and were killed by serpents. (10:9)