Define electric flux. Is it a scalar or a vector quantity?

Part (a)
Step 1: Definition of electric flux
Qualitative Definition:
The Electric flux is proportional to the number of field lines passing a given area in a unit of time. This definition cannot be used for calculating the exact value of flux, it is used only for the comparison of flux through two surfaces.
Quantitative Definition: Magnitude of Electric flux is given by
ΔΦ=∫→E.→dS
For plane surface and uniform Electric field, the above equation becomes:
ΔΦ=→E.→S=EScosθ
It is a scalar quantity.
Step 2: Electric flux through square
Suppose a cube enclosing the charge q of sided.
Hence according to Gauss's law, the electric flux through the cube is
q/εo
The given case can be considered as one of the face of such a cube.
By symmetry, the flux through the face is 1/6th of the flux through the cube.
Hence flux through the square face = q/6εo
Part (b)
Electric flux through square when the side is doubled
Now, the charge is placed at a distanced from the centre of square. Also, the side of the square is 2d in this case.
In this case, the charge will be at the center of a cube of side 2d and the square will be one of its face.
According to a similar analysis as shown in Step 2 the electric flux through the face is:
q/6εo
Hence there will be no change in the electric flux.