In "Romeo and Juliet", do Benvolio and Mercutio have last names? Does it ever explain how old any of the characters are?I have to write an article...

To answer your first question, the last names of Benvolio, Mercutio, and Paris are never mentioned.  We do know, however, what families the three men are from.  Benvolio is Romeo's cousin, therefore he is a Montague.  Mercutio and Paris are both relatives of Prince Escalus so although their last names are never alluded to, you do know that they are related to the rulers of Verona.  As for their ages, we also do not get that information -- except for that of Juliet.  After a conversation between the Nurse and Lady Capulet, the reader finds out that Juliet is almost 14 years old; however, the ages of the other characters, including Romeo are not given.  It is generally assumed that Romeo is in his late teens.