Yes.The average velocity of a moving object can be zero.You see , average velocity is displacement divided by time.Displacement being the shortest distance between two points travelled or the position vector of the place you are currently at, displacement can be zero.For eg. if you travel in a circle and come back to the same point from where you started , your displacement is zero.Hence irrespective of the time you took to come back to the point,your average velocity will be zero as zero divided by anything will be zero.Your average SPEED on the other hand will be non-zero because that is distance divided by time and distance is a scalar not a vector and in this case your distance is non-zero as you have actually travelled the entire circle.The fact that your initial and final position vector coincide does not make a difference to the DISTANCE that you have travelled.
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Sure it can. The average has to be taken over some interval of time. If in that interval the object ends up where it started, then its average velocity is zero. Its average speed, on the other hand, must be positive if it moved. Pay careful attention to the difference between velocity and speed, and look at the definition of each.
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If the velocity is measured as a function and is a parabola, then if two points of average are taken from opposite sides of the parabola, the average will be 0.
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velocity is vector quantity and speed is a scalar quantity.so zero average velocity is possible in case of velocity but not in speed
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it most certainly can. however, zero average velocity does not equal zero displacement. zero average velocity equals zero average displacement.