In sentence 1, that acts as a relativizer (relative pronoun). It may be dropped (in any register) because it acts as the direct object of the verb in the relative clause. It could not be dropped in formal English (though it often is in informal spoken English) if it were the subject of the verb in the relative clause:
✲ It's the same girl Ø took our family photo.
In the remaining sentences, that acts as a subordinator (subordinating conjunction). In sentences 2, 3 and 4, that may be dropped because the subordinate clause which it heads is the direct object of the verb in the main clause and is in its ordinary position immediately after that verb.
If that played another role, such as subject, or if the subordinate clause were displaced to another position, that could not be dropped, because it would not be clear that it is in fact a subordinate clause:
✲ Ø he's protected by his family is understood by Alex ... The clause falls at the beginning of the sentence, before the verb is, because it has become the subject. That cannot be dropped.
✲ I came to know some eight or ten days after I got the report Ø you got stuck in traffic. ... Here the subordinate clause has been separated from its governing verb by a fairly long ('heavy') adverbial phrase . You could probably get away with dropping the that in speech, but it cannot be dropped in formal writing.
In sentence 5, and in these rewrites of sentences 4 and 5, the situation is a little different: These subordinate clauses are predicative complements of BE, and in speech that may be dropped even if the clause is moved to the front. In writing it's permitted, but not advisable; you really want to give the reader as many clues to your structure as possible:
? What many people are saying is Ø they saw a ghost.
? Ø I need help from you is the reason I'm helping you.
In other uses, as a demonstrative adjective or a demonstrative pronoun, that may not be dropped.
I want that puppy. but not ✲ I want puppy.
John took that from Shakespeare. but not ✲ John took from Shakespeare.
✲ marks an utterance as unacceptable
? marks an utterance as possibly unacceptable
Ø marks the place where that is omitted
I gave him the money is simple past. You can use it to specify something that happened in the past: you can also specify when it happened, either exactly:
I gave him the money at 6pm
or approximately:
I gave him the money this evening
I gave him the money at about 6
I gave him the money by 6pm.
or not at all:
Yes, I gave him the money.
I had given him the money is past perfect simple. We use this when we are talking about something that had already happened before some event or action in the past. The event isn't usually a specific time: it is a part of the story, for example:
I had given him the money before I got your message
I had already given him the money, but he kept on shouting at me
Here is some more information about simple past and past perfect.
The first sentence, using simple past, is the idiomatic way of saying this. The second sentence doesn't sound right, because after you have said it I am waiting for the event that it happened before: I am not impressed by by 6pm: I want to know what happened next!
The second pair of questions present a different problem.
By 5 PM I gave him the book.
By 5 PM I had given him the book.
Starting with by 5 pm makes these sentences look odd on their own: the seem to need a clause before or after them, for example:
I was working all day, and by 5pm I had given him the book.
The deadline was 6pm, but by 5pm I had given him the book.
By 5pm I had given him the book, and then I went home.
Best Answer
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.
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:
Therefore you should use whether (that is used for noun clauses derived from statements).
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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.-
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.