Remember the day of salvation is today -- there is no need to wait for tomorrow. The grace of God is freely and fully offered today! Grab on with both hands and join the ride.
St. Paul lived a difficult and challenging life. His work often caused riots. On multiple occasions people tried various methods to kill him -- in Damascus, in Jerusalem, in Ephesus and so forth. It seems the simple unvarnished message of the love of God freely given through Jesus Christ was met with anger, hatred and violence. He shares all of this with the Corinthian church in order to get their attention and, I suspect, to help them listen to what he is trying to tell them.
Do no be yoked together with unbelievers. This passage, over time, has been used to justify a lot of harsh decisions. The point Paul is making is that we should not willingly enter into partnerships with people who do not share the same values as you do. In the case of marriage see 1 Corinthians 7. Paul says that if someone becomes a Christian but their spouse does not to be patient and not abandon the unbelieving partner. The issue here is not that kind of marriage situation but willingly entering into a partnership with someone you know is still practicing idolatry. A friend of mine called this "missionary dating" and it is never a good idea.