What is the function of electric water pump, i.e does it push or pull water or both?
Depending on the pump design it can push, pull or do both. In reality, all pumps are pushers, since even a pulling pump (e.g., sucking water up a drinking straw) is simply removing pressure on the pump side so that greater pressure on the pumped fluid at the other end of the line can push it into the pump.
Positive displacement pumps (e.g., gear pumps, peristaltic pumps and piston pumps) are typically considered "pushers," even though they are pulling the pumped material into the pump before pushing it out. You could use this intake to pump materials, in which case, I guess, you would have a "puller."
A centrifugal pump could be considered a pusher or puller, depending on which end the longest line is connected to. Then there is the electrodynamic pump, with no moving parts, which forces electrical current through the pumped media at right angles to an applied magnetic field, to induce a forward force in the conductive fluid itself: hard to characterize that one.
If any pump could be classified as a pulling pump it would be a pump working on the Venturi/Bernoulli effect. Pulling pumps which are open to the atmosphere have a theoretical pulling limit of 14.7 psi. This is because the real action is pushing by the atmosphere on the end away from the pump, and atmospheric pressure at sea level is 14.7 psi.
I have a simple water pump that is an attachement to the Black end Decker electric tool. It is a small, 15cm or so disk, evidently rotating chambers inside to create a suction vacuum. So this one pulls the water.