Can I get a train from Guangzhou East station to the North one? And how much is the fare?

Hi, I'm afraid you cannot take a train from the east station to the north one. As for the route, here is my suggestion:
At the East Railway Station, you can walk to the th East Bus Station to take the East Station - Huadu exlusive bus line. Then you need get off at Erqi Huadu Bus Station. After your getting off, the north station is only about 200-250 m from where you are.