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.
He said that he was not feeling well, so I suggested to him that he should see a doctor.
Or you could make the sentence shorter because the "to him" is implied:
He said that he was not feeling well, so I suggested he see a doctor.
Best Answer
Both sentences seem to be correct. However, it depends on who you are addressing. If you are talking to one person, the first option would be the best choice. If you are talking to multiple people, or a whole company, then you should use option 2.
As a British person, I recognize that "keen" is a word mostly used in Britain. If you are talking to somebody who's not from Britain, maybe change "keen" into one of keen's synonyms.