Does Gauss's Law depend only on charges inside a closed surface or around it?

Why doesn't Gauss Law hold true for calculating electric field for every charge distribution?

Will Gauss’ Law still apply if the Gaussian surface passes through a charge?

Given below are two statements:

Statement I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.

Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (<R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero.

In the light of the above statements, choose the correct answer from the option given below:

If ${\text{?}\mathrm{}}_{\mathrm{s}}\stackrel{?}{\mathrm{E}}\cdot \stackrel{?}{\mathrm{d}\mathrm{S}}=0$  over a surface, then:

The total charge enclosed in an incremental volume of 2 × 10^-9 m³ located at the origin is _________nC, if electric flux density of its field is found as

D = e^-x sin <!-- [if gte mso 9]><xml> </xml><![endif]-->  $y\widehat{i}-e^{-x}cosy\widehat{j}+2z\widehat{k}C/m^2.$