Can the displacement of a particle be zero when the distance travelled is not zero?

$A$ girl walks along a straight path to drop a letter in the letterbox and comes back to her initial position. Her displacement-time graph is shown in the figure. Plot a velocity-time graph for the same.

Can a body have constant speed and still be accelerating?

State which of the following situations are possible and give an example of each of these:
$(a)$ $A$ body moving with constant acceleration but with zero velocity.
$(b)$ $A$ body moving horizontally with an acceleration in the vertical direction.
$(c)$ $A$ body moving with a constant speed in an accelerated motion.

If the displacement of an object is proportional to the square of time,then the object moves with

Give one example for each of the type of motion when
$(i)$ acceleration is in the direction of motion.
$(ii)$ acceleration is against the direction of motion.
$(iii)$ acceleration is uniform.