Question

What is effective nuclear charge of S2- and S? Does the Z eff differs from ions and atoms of the same element

Answer 1

Effective nuclear charge is an estimate of the charge experienced by the valence electrons. There are several ways of constructing it. The easiest is just to ask what the charge on the "core" is if you strip off all the valence electrons. Sulfur has 6 valence electrons, so the charge on the core without them would be +6. So that's one estimate.

A more sophisticated estimate takes into account the fact that the 3s electrons in sulfur will slightly screen the 3p electrons, because the former spend more time closer to the nucleus (between the nucleus and the 3p electrons). Using Slater's Rules, you come up with an effective nuclear charge of +5.5 for sulfur.

It's hard to be 100% sure what you're expected to say for S-2. If the idea is to ask what the Zeff that the 8 valence electrons in that ion feel, which is what I would guess, then the answer is the same. (The valence electrons will screen each other a tiny bit, but this is pretty subtle effect, and I wouldn't expect your instructor to be asking about that, unless you are in a upper division p-chem class.)