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.
