Can an object have zero velocity but non-zero acceleration? can it have zero acceleration and nonzero velocity? support your answer.

Both can be true.
The first can be true in the cause of an object being thrown up, for example. If I throw a baseball up into the air, it has a constant downward acceleration of 9.81 m/s^2 (g), but when it reaches the top of the arc, it has zero velocity.
The second can be true for an object not under the influence of any net outside force. You may have seen Newton's first law before:
"Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."

If an item is floating through a volume of space with no gravity effects and no air resistance, it will continue to move at a constant velocity.