Can an object have zero velocity but nonzero acceleration?
can it have zero acceleration and nonzero velocity?
why?

Yes in both cases.
The first case is visible when an object's instantaneous velocity is 0 but its acceleration has a non-zero value. This occurs when velocity and acceleration are in opposite directions. Its is visible when an object is thrown upwards. There comes a point where it is stationary in the air with velocity 0; however, the acceleration due to Earth's gravity is still acting on it.
An object traveling at constant velocity has 0 acceleration.