He was probably so hungry that he ate too fast and it came back up just as fast.
They will cry in their crate for awhile, but they also need to be taken out periodically to pee. Their little bladders cannot hold their pee all night long. At his age, he can hold it for 3 hours, tops. So, yes, when he's peed, put him back in his crate so that he will know it's nighttime. He will eventually learn to go to sleep on his own. It will take several weeks or months for him to be able to hold his pee all night long.
Good luck!