Which information cannot be drawn from average velocity?

Is the statement "$A$ particle can have zero speed but non-zero velocity" true or false? Explain.

$A$ car moves from $X$ to $Y$ with a uniform speed $v_1$ and returns from $Y$ to $X$ with a uniform speed $v_2$. The average speed for this round trip is

$A$ person travels $x$ distance with velocity $v_1$ and then $x$ distance with velocity $v_2$ in the same direction. The average velocity of the person is $v$. Then the relation between $v, v_1$ and $v_2$ will be:

$A$ particle moves along a straight line along the $x$-axis. Its position $(x)$ versus time $(t)$ graph is shown in the figure [$x$ in meters and $t$ in seconds]. Its average speed during this motion is (in $\text{ m/s}$)

Explain clearly, with examples, the distinction between
$(a)$ magnitude of displacement over an interval of time, and the total length of path covered by a particle over the same interval.
$(b)$ magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval].
Show in both $(a)$ and $(b)$ that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only].