smc

Statement $1$ is true. A $180^{\circ }$ rotation about the point half way between an up-facing square and a down-facing square will yield the same figure. Statement $2$ is also true. A translation to the left or right will place the image onto itself when the figures above and below the line realign (the figure goes on infinitely in both directions). Statement $3$ is false. A reflection across line $\ell$ will change the up-facing squares to down-facing squares and vice versa. Finally, statement $4$ is also false because it will cause the diagonal lines extending from the squares to switch direction. Thus, $\boxed{2}$ statements are true.