Several questions that pop to my mind are as follows:

What happens to Friar Laurence and Juliet's nurse after the play ends? Is the nurse fired for her part in the plot to marry Juliet to Romeo? Or is the family willing to forgive her? What would she have done after Juliet married Paris, and what will she do now?

Why are the Montagues and the Capulets feuding? Shakespeare's point appears to be that the reasons for the feud have been long lost in the mists of time, making it all the more irrational that the families are fighting, but what, at first, put them at odds?

What does Benvolio do when his two best friends are either killed or banished? Does he find a girlfriend? Or does he become depressed?

Why is Juliet so attached to Tybalt that for a moment she hates Romeo for killing him? What is the backstory between the two cousins? Were they close friends growing up?

You are correct.  There are sections of the play that Shakespeare leaves up to the reader and never explicitly says.  

One such ambiguous part is exactly how old Romeo is.  The reader is told that Juliet is 13, but is never told how old Romeo is.  We know that he is a young man, but that could mean anywhere from 15-25. 

Shakespeare never explains exactly why the Capulets and Montagues are fighting.  The reader knows that the families are rich and influential.  We know that the feud has been going on for a long time and that the feuding is well known to the public. 

I've always wondered why Romeo isn't close to his family.  He is quick and ready to throw off his family name and fortune for Juliet.  He also doesn't seek advice from his father or mother or family servant in the way that Juliet does.  Instead he goes to Friar Laurence.  

Friar Laurence obviously knows his way around herbs and poisons.  Why then does Romeo visit an apothecary instead?