My thoughts on your questions about this passage that you presented:
Mike Roger told CNN that publication was "a terrible idea" and said "Foreign leaders have approached the government and said, 'You do this, this will cause violence and death.'"
1. Setting off the phrase "a terrible idea" with a quote and unquote is done when the writer wants to emphasize that it's somebody else's and not his own utterance. Without that quote and unquote, there's a risk that the phrase might be construed as the writer's own making, for which he might be viewed as unfair or opinionated.
2. Yes, in the interest of parallelism and for a better-flowing statement, the writer should have uniformly constructed that sentence as indirect speech, as follows:
Mike Roger told CNN that publication was "a terrible idea" and that foreign leaders have approached the government and said, "You do this, this will cause violence and death."
I think the original sentence just happened to be badly constructed owing to the usual exigencies of TV journalism.
3. No, even if the whole statement is rendered in indirect speech speech as was done in Item 2 above, there's really no need to back-shift the tense of the second declaration from the present perfect "have approached" to the past perfect "had approached." Setting off the second declaration in quote and unquote, "Foreign leaders have approached the givernment and said, 'You do this, this will cause violence and death'", was evidently done by the writer to avoid the complication of back-shiftng tenses, and that indeed was the right thing to do in this particular instance.
4. No, the writer's clumsy use of the form "And said , 'If you do this...'" was grammatically and stylistically clumsy and definitely no better than just constructing the whole thing as indirect speech, as was shown in Item 2 above. Even better, that statement could have been better organized and rendered in two sentences, as follows:
Mike Roger told CNN that publication was "a terrible idea." He said: "Foreign leaders have approached the government and said, "You do this, this will cause violence and death.'"