What is true for an electric dipole placed in an electric field generated by a point charge?  

Torque on the dipole due to electric field may be zero 

As the electric field is non-uniform. So the magnitude of forces on charge q and -q is not equal as it depends on the strength of the electric field. Therefore net force is not equal to zero.

If an electric dipole is placed in an electric field generated by a point charge then the torque on the dipole due to the field may be zero when the dipole moment and electric field are parallel to each other.