One example of Velocity is that if you are running in the same direction, your speed and velocity is the same. But if you are running AROUND the track, your speed is the same but your velocity is changing.
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An example problem involving speed is calculating the average speed of a car that travels 100 miles in 2 hours. An example problem involving velocity is determining the velocity of a ball thrown upward with an initial velocity of 20 m/s at a height of 40 meters above the ground.
A non-example of velocity would be a stationary object at rest. Velocity specifically refers to the speed of an object in a specific direction, so an object that is not moving does not have velocity.
Acceleration
Yes, an object moving at a constant velocity has zero acceleration even though it has a non-zero velocity. For example, a car driving at a steady speed on a straight highway has a constant velocity but zero acceleration.
Velocity is directional, so if something is accelerating in the opposite direction from the one it is moving it, there will come a point where it has 0 velocity but still has accelerating. If you throw a ball at the ground and it bounces, for example.