Please help me to find three examples of hyperbole in the Romeo and Juliet as well as three quotes that demonstrate loyalty.

Here are three examples of hyperbole (also called overstatement because it emphasizes truth through exaggeration):

After learning that he will be exiled from Verona for slaying Tybalt, Romeo says, "There is no world without Verona walls, / But purgatory, torture, hell itself" (3.3.18-19).  He means that to him, Verona is the world and to be anywhere else is to feel as though he is in hell. 

When Romeo watches Juliet on her balcony, he says...

Here are three examples of hyperbole (also called overstatement because it emphasizes truth through exaggeration):

After learning that he will be exiled from Verona for slaying Tybalt, Romeo says, "There is no world without Verona walls, / But purgatory, torture, hell itself" (3.3.18-19).  He means that to him, Verona is the world and to be anywhere else is to feel as though he is in hell. 

When Romeo watches Juliet on her balcony, he says that "The brightness of her cheek would shame those stars, / As daylight doth a lamp; her eyes in heaven / Would through the airy region stream so bright / That birds would sing and think it were not night" (2.2.19-23).  There are actually two examples of hyperbole in these lines.  First, Romeo says that Juliet's beauty seems to shine even brighter to him than the stars, just as the sun shines brighter than a lamp.  Second, that her eyes are so bright that the birds would think it is daytime and begin to sing, even though it is really night.

Here are three quotes that demonstrate loyalty:

Romeo is loyal to Juliet, his new (secret) wife; so much so that, when Tybalt comes to duel with him, he refuses to fight.  He says that he "love[s] [Tybalt] better than [Tybalt] canst devise," that he "tender[s] / [Tybalt's] name as dearly as [his] own [...]." (3.1.70.72-73).  Thus, he refuses to fight Tybalt, his wife's cousin, because he is loyal to her and to her family.  Even when Mercutio accuses him of behaving dishonorably, he remains loyal to her.

The nurse is loyal to Tybalt, at least immediately after his death, saying, "O Tybalt, Tybalt, the best friend I had!" (3.2.67).  Frankly, the nurse seems loyal to everyone, all at once sometimes!  She's very loyal to Juliet, and even Romeo at times, but she eventually agrees with the Capulets' in her advice to Juliet to marry Paris.

Just prior to this, however, the nurse does stick up, quite loyally, for Juliet when her father is berating her for her disobedience.  She cries out, "God in heaven bless her! / You are to blame, my lord, to rate her so" (3.5.176-177).  The nurse defends her charge, standing up for her when not even her own mother would.