Which line of dialogue from act iii, scene i of romeo and juliet most foreshadows that mercutio’s death will lead to other tragic events in the story?
benvolio: o romeo, romeo! brave mercutio’s dead;
that gallant spirit hath aspir’d the clouds,
romeo: this day’s black fate on more days doth depend;
this but begins the woe others must end.
tybalt: thou wretched boy, that didst consort him here,
shalt with him hence.
prince: romeo slew him, he slew mercutio;
who now the price of his dear blood doth owe?

The correct answer is - Romeo: This day’s black fate on more days doth depend; / This but begins the woe others must end.

When you translate these lines into contemporary English, they basically mean that 'what happened today will have a negative effect on the days to come.' So he is explicitly saying that Mercutio's death will lead to tragic events further down in the play, and he was right. Eventually, both lovers died.

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.