When does the torque acting on an electric dipole in a uniform electric field become zero?

When three electric dipoles are near each other,they each experience the electric field of the other two,and the three-dipole system has a certain potential energy. The figure below shows three arrangements $(1)$,$(2)$,and $(3)$ in which three electric dipoles are side by side. All three dipoles have the same magnitude of electric dipole moment,and the spacings between adjacent dipoles are identical. If $U_1$,$U_2$,and $U_3$ are potential energies of the arrangements $(1)$,$(2)$,and $(3)$ respectively,then:

Consider a positively charged infinite cylinder with uniform volume charge density. An electric dipole consisting of $+Q$ and $-Q$ charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure,the dipole will experience,

An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \text{ C}$ separated by a distance of $3 \text{ cm}$ is placed in an electric field of $2 \times 10^5 \text{ N/C}$. The maximum torque acting on the dipole is:

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(+d, 0)$ respectively of an $(x, y)$ coordinate system. Then:

$A$ dipole having a dipole moment $p = 4 \, C-m$ is placed at the origin along the $x$-axis. $A$ point charge $q = 8 \, \mu C$ is fixed at $(4, 0, 0)$. Now,the dipole is rotated by an angle of $\frac{\pi}{2}$. Find the work done (in $mJ$) in rotating the dipole.