Continuity mistake: When Killian Jones, a.k.a. Captain Hook, is talking to Emma on the street, he points to one of his rings and reveals that it belonged to a man who insulted him by calling him "One Hand Jones." According to Hook, he killed the man in front of his wife, and took his ring as a trophy. However, as seen in 2-04 "The Crocodile", Hook was already wearing this ring before he lost his hand to Rumplestiltskin. This is best seen while he and Milah are drinking and gambling at the tavern: In the shot of the dice landing on the table, you can see Hook's hand resting on the table, wearing the same ring.
Revealing mistake: As Hook is chasing King Arthur through the woods, there is a shot of Arthur running, where you can see that the one running is not Liam Garrigan, but his stunt double. In the next shot, Hook is hot on Arthur's heels and you can see that it is Colin O'Donughue's stunt double who is chasing him.
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.