At first none of the examples sounded good to my ear, but after I looked it up it seems that the 2nd and the 3rd are correct.
Many discuss the topic that whether medicine has true benefit on our society.
Whether is a subordinating conjunction. That is also a conjunction. Pilling up conjunctions one after another does not serve a purpose, and it is grammatically incorrect. Both of these conjunctions can be used to introduce a noun clause, but in your example the noun clause is derived form a yes/no question:
Does medicine have true benefit on our society?
Therefore you should use whether (that is used for noun clauses derived from statements).
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Many discuss the topic of whether medicine has true benefit on our society.
Google books shows evidence of "... of whether..." construction usage, e.g. in: "...the question of whether the pure self can be conceived of in unity with a living organism." At the same time
LDOCE gives examples of the construction "topic of". Since these two were my main concerns, the sentence should be correct.
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Many discuss the topic on whether medicine has true benefit on our society.
Again, there is evidence of usage of the phrase:
topic on whether, although there are only 68 hits, which would indicate that this phrase is used rarely.
Finally, Many question whether medicine brings a true benefit to the society would be my personal preference, but there are many ways to phrase this thought.
Do not is present simple and in narrative sentences is supposed to mean a constant and regular action or some mental process or state to which continuous tense is not applied. It is kind of out of place in this context. Please refer, say, to Wiki for more information or just google "present simple vs present continuous".
Now about the rest of options.
If you have already decided you do not want to show "this" in the report and want to underline this is your plan you are going to follow, you can say:
[..] we are not showing this in the report.
Or, if you are not quite sure yet but are inclined not to show:
[..] we are not going to show this in the report.
Will not has a slight emphasis that the solution has just been done by you. You decide not to show this and immediately say:
[...] we will not show [...]
however, it also mean just the mere fact we will not show this in the report. Refer to this article about differences between be doing, be going to do and will do.
As for need not and should not, you correctly described their meaning, which one to use is up to you and depends on what you want to say.
PS For further reading, you may want to learn more about the phrase to be going to, modal verbs like should, owe, must etc, as well as aspects of present continuous use with regard to the future actions.
Best Answer
We often use whether-clauses to represent closed questions. This means they often represent questions which have the answer yes or no.
So there are two possible answers to the question Should I sell my stock position?: YES and NO.
In English, when a whether-clauses represents a closed question, we do not need to represent the no option in the clause. (In many other languages you do need to represent the no option).
However, although we don't represent the no option, we can if we want to. This does not change the meaning of the sentence at all. There are two ways we can do this:
In the first example, we see the words or not appearing after the word whether. In the second example, these words appear at the end of the clause instead. Both of these examples are grammatical.
In English, sentences (1), (2) and (3) are all grammatical and all mean the same thing. For this reason both of the Original Poster's examples are grammatical and also have the same meaning.
Grammar note:
We can also use whether-clauses to make special conditionals called exhaustive conditionals. When we use whether-clauses in conditionals, they MUST include all the possible outcomes of the situation—otherwise they are ungrammatical. Usually this means that they must contain the words or not: