Continuity mistake: When Henry is in New York and trying to conjure magic by the fountain, you can see that the building in the background says Vancouver Art Gallery on the top. (00:23:15 - 00:24:57)
Continuity mistake: As Dr. Jekyll leads David, Hook, Mary Margaret and Zelena through the marketplace while they try to escape from Mr. Hyde, as Hook says, "Next time, try an aggressive bunny rabbit", he is wearing a ring on his index finger. Two shots later, as they group heads into the alley, the ring is gone (only three seconds have passed, and since Hook only has one hand, he could not have taken it off that quickly). In the next shot, the ring is still missing, and the camera stays on Hook the whole time, but in the next shot, the ring has mysteriously reappeared.
Continuity mistake: When Emma and the others return to Storybrooke, in several shots, like when Regina exits Emma's car, the Storybrooke Cannery appears in the background, painted in white. However, when the magic is released from the Olympian crystal, there is a shot where we see a wave of magic move through Storybrooke Main Street, where the top half of one of the cannery buildings is painted in red.
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.