When does the magnetic flux become zero?

Consider a closed loop $C$ in a magnetic field as shown in the figure. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula $\phi = \sum \vec{B}_i \cdot d\vec{A}_i$. Now,if we choose two different surfaces $S_1$ and $S_2$ having $C$ as their edge,would we get the same answer for the magnetic flux? Justify your answer.

Which of the following do not exist?

The radius of a coil of $N$ turns is $R$. If the plane of the coil is placed parallel to a uniform magnetic field $B$,then the flux linked with the coil is:

$A$ square loop of side $1\,m$ and resistance $1\,\Omega$ is placed in a magnetic field of $0.5\,T$. If the plane of the loop is perpendicular to the direction of the magnetic field,the magnetic flux through the loop is $\dots\dots$ weber.

$A$ circular loop of radius $R$ carrying current $I$ lies in the $x-y$ plane with its centre at the origin. The total magnetic flux through the $x-y$ plane is: