Zero relative velocity to another object, sure no problem.
Zero absolute velocity, not possible as there is no absolute reference to compare to.
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Yes, it can happen. when the velocity is momentarily zero while an object is changing from moving in the positive direction motion to the negative direction; the object obviously will stop at one point, but will still have a constant acceleration.
Velocity. When an object is standing still at position p, the velocity dp/dt = 0 is zero.
An object which is not changing in it's position in space. In simply it is at rest
Yes, of course; but it will only have zero velocity for one infinitesimal moment. Check your calculus text.
Yes. Zero velocity is a velocity; if it is always zero then it is a constant velocity.