What is the correct option for an electric dipole placed at the centre of a sphere?

Electric Field is non-zero anywhere on the sphere. 

The electric field is the resultant field effect due to all charge. So the field is not zero inside sphere or any other point on the sphere.

A dipole contains two equal and opposite charge. So total charge inside the sphere will be zero. By Gauss's law, the flux across a surface is depends on the charge inside the surface. As total charge is zero inside the sphere so the flux through the sphere will be zero.