If a young man sows his wild oats, he has a period of his life when he does a lot of exciting things and has a lot of sexual relationships. for e.g. He'd spent his twenties sowing his wild oats but felt that it was time to settle down.
If a person is the spitting image of somebody, they look exactly alike.('Spit and image' is also used and some suggest it is a hasty pronunciation of "spirit & image", to suggest that someone completely resembles someone else. Example: He's the spirit & image of his grandfather.)
A Sputnik moment is a point where people realise that they are threatened of challenged and have to redouble their efforts to catch up. It comes from the time when the Soviet Union launched the first satellite, the Sputnik 1, and beat the USA into space.