The wave is moving to the right. That means that the portion on the right of the point Y has already passed Y. So just before this picture was taken, the point Y was higher up, and in a few moments, it will be lower down. Therefore, the water at point Y is moving downwards.
As for the second part, think what would happen if you were neck-deep in the water, being lifted up and moved down in time with the waves. When would you be motionless?