The reason behind which 'plane' the nucleophile attacks has to do with Molecular Orbital Theory.
But here's a short explanation for this: the C-X bond appears because two atomic orbitals interact to form two molecular orbitals: a filled bonding orbital ($\sigma$) and an unfilled anti-bonding orbital ($\sigma^*$).
For the C-X bond to break, the nucleophile has to attack $\sigma^*$, which means that the nucleophile has to get a good overlapping of its filled orbital with the unfilled anti-bonding orbital of C-X. Because of this attack, the C-X bond breaks and the C-Nu bond forms.
To give you an image of where the anti-bonding orbital is located, think of the C-X $\sigma$-bond; behind that bond on the carbon side, there lies the biggest portion of $\sigma^*$ (see Ivan's image). If we consider that, this orbital intersects the 'black plane' that you were talking about.
Therefore, the nucleophile can't attack the other 'planes' besides the 'black plane' because that doesn't assure a good overlapping between orbitals.
As for the change in configuration, in primary alkyl halides (the example you gave) we don't have a change of configuration because the carbon atom that's bonded to the halogen is not chiral.
But with a chiral compound, (i.e. (R)-2-chlorobutane), we get a change in configuration because the nucleophile attacks 'from the back', reversing it (i.e. (S)-butan-2-ol.)