For an electron arrangement diagram, is it necessary to show the inner electron shells or is it customary to only show the valency electrons? Which electron arrangement diagram is correct? The one that shows all electron shells or the one that only shown the valence electron shell?
Both are correct: for $\ce{Cl-}$, the inner set of electrons would be implicit, as $\ce{Cl}$ has 17 electrons. The point of drawing these orbital diagrams, especially in a molecular context, is to show the nature of bonds and to show how the octet/duplet rules are being followed. 

If you have difficulties in using the second diagram (finding it harder to read or are confused by the similarities in $\ce{H}$ and $\ce{Cl}$), you should use the first diagram.