Or, can a body have zero velocity but non-zero acceleration?
Yes. When a body moving in a certain direction is being acted upon by a force in opposite direction, then the body decelerates and ultimately comes to stop. At that time, its velocity is zero but since the opposing force is still acting, the body has acceleration in the direction of the force.
[Read: Motion in a Straight Line]
For example, when a body is thrown vertically upward, at the highest point, it has zero velocity but its acceleration is equal to acceleration due to gravity $(g)$.
[Read: Motion Under Gravity]
Similarly, in simple harmonic motion, a body has zero velocity and maximum acceleration at the extreme point.
A player hits a baseball at some angle. The ball goes high up in space. The player runs and catches the ball before it hits the ground. Which of the two (the player or the ball) has greater displacement?