Hi BenjaminTW,
Glad to hear that you got the question right in the end! Your thinking generally seems correct overall, though I'll review some of the conditional reasoning that we can diagram.
For "The only purpose this disclaimer could serve is to provide legal protection for the company," we can diagram:
Disclaimer has purpose Purpose is legal protection
With that in hand, a worthwhile next step is to diagram the contrapositive as well:
~(Purpose is legal protection) ~(Disclaimer has purpose)
Then we have the next sentence, "But if the e-mail elsewhere suggests that the client do something illegal, then the disclaimer offers no legal protection." This can be diagrammed as:
Elsewhere recommends illegality Disclaimer gives no legal protection
The contrapositive of which is:
~(Disclaimer gives no legal protection) ~(Elsewhere recommends illegality)
Finally, it concludes, "So the disclaimer serves no purpose."
With these premises and conclusion, the question stem is asking for an answer that, if added as a premise, would be sufficient to permit the conclusion to be drawn. Let's look at the correct answer choice, (A): "If the e-mail does not elsewhere suggest that the client do anything illegal, then the company does not need legal protection."
I think I follow what you're saying about the word "elsewhere." As I read this paragraph, "elsewhere" is referring to anything other than the disclaimer. This seems to be the case because the sentence before the one mentioning "elsewhere" is discussing the disclaimer. And answer choice (A) utilizes the same word as well. That answer choice can be diagrammed as:
~(Elsewhere recommends illegality) ~(Need legal protection)
Or in its contrapositive form:
Need legal protection Elsewhere recommends illegality
This makes sense because we can add this premise to what we already had:
~(Disclaimer gives no legal protection) ~(Elsewhere recommends illegality) ~(Need legal protection)
which can be shortened to:
~(Disclaimer gives no legal protection) ~(Need legal protection)
or as the contrapositive:
Need legal protection Disclaimer gives no legal protection
In other words, the disclaimer serves no purpose because if the company needed legal protection, the disclaimer doesn't offer legal protection.