Continuity mistake: When Emma finds Snow White's glass coffin, there's a hole in the lid. In the overhead shot, the hole is rather small, but in the shot from inside the coffin, the size of the hole has changed dramatically. In the next shot, it is small again. (00:20:15)
Continuity mistake: In "That Still Small Voice", when Regina throws the piece of glass down the shaft, it lands on the rest of Snow White's glass coffin, which has several holes in it. When Emma finds the coffin in this episode, there is only a single hole in the glass, and the ends of the coffin (made of wood), are much smaller. (00:20:15)
Answer: He knows who she is because he knows that the fairy tales are true. He was also shown to sneak out to go see Emma or someone else. Sometimes he succeeded, sometimes he didn't. This is how he knew to look for her despite his strict mother.