How does Mercutio serve as a dramatic foil to Romeo in Romeo and Juliet? (List 3 traits for each character and provide textual evidence for each.)

Mercutio is a foil to Romeo in several ways. The two close friends are alike in being young, passionate, and sometimes impulsive youth of Verona who both have a way with words. Three ways they are different, however, are as follows:
First, Romeo is in love with love. Romantic love is his chief pursuit in life. In contrast, Mercutio is jaded and cynical about love.
We know that Romeo is in love with love from the very start of the play. Lord Montague seeks out the level-headed Benvolio because he is worried about Romeo's mooning about, wandering around at night, and sleeping during the day. When Benvolio confronts Romeo in act 1, scene 1, Romeo can't stop talking about love, saying,

Love is a smoke raised with the fume of sighs;
Being purged, a fire sparkling in lovers' eyes;
Being vexed, a sea nourished with loving tears.

Romeo is lovesick for Rosaline, who doesn't return his love and admits, "In sadness, cousin, I do love a woman."
Not long after this, of course, Romeo will meet Juliet at the Capulets' party and fall head over heels in love with her, forgetting Rosaline and wanting to marry Juliet the next day. Romeo shows himself a master of passionate love language, which reflects his deeply felt emotions, in the balcony scene with Juliet after the masquerade ball. You can find many examples of romantic love language in this scene in act 2, scene 2. Here are a few:

O, it is my love!O, that she knew she were!

He then refers to Juliet in exaggerated yet always sincere love language, saying she is so bright with beauty the birds would mistake her for the sun and wake up in the middle of the night. He also longs to touch her cheek:

The brightness of her cheek would shame those stars
As daylight doth a lamp. Her eye in heaven
Would through the airy region stream so bright
That birds would sing and think it were not night.
See how she leans her cheek upon her hand.
Oh, that I were a glove upon that hand
That I might touch that cheek!

This is language you will never hear from Mercutio. He takes a harder, more cynical view of love and is more prone to connect it with sex and make jokes about it. He loves to make bawdy sexual puns. In act 1, scene 4, the cynical Mercutio says to Romeo,

If love be rough with you, be rough with love.
Prick love for pricking, and you beat love down.

in act 2, scene 4, Mercutio runs into Romeo, not knowing that Romeo has fallen for Juliet, and is delighted to see his friend has come back to life. Mercutio says to him that love is foolish, again showing his different view of romance (and his words are also ironic, since love is what has perked Romeo up):

Why, is not this better now than groaning for love? Now art thou sociable, now art thou Romeo; now art thou what thou art ... for this drivelling love is like a great natural [fool], that runs lolling up and down to hide his bauble [cheap trinket, but also a sexual innuendo] in a hole.

Second, Mercutio enjoys a fight for the sake of a fight. In act 3, Mercutio goes out looking for a brawl on a hot summer day. Romeo, in contrast, never shows much interest in the the street fighting that breaks out between the Capulets and the Montagues, even before he falls in love with Juliet. He will sword fight and do it well, but only when he has a score to settle.
While Romeo, who has just married Juliet, tries to stop the fight between Mercutio and Tybalt, Mercutio insists on fighting, saying, in act 3, scene 1, of Romeo's peacemaking efforts,

O calm dishonourable, vile submission!

He ignores Romeo's words meant to prevent a fight, stating to Tybalt,

Will you pluck your sword out of his pilcher by the ears? Make haste, lest mine be about your ears ere it be out.

It must be emphasized that while Romeo does fight and kill both Tybalt and Paris, in both cases he feels he has a strong reason; he does not, like Mercutio, simply go swaggering about looking for trouble.
Finally, Romeo is more likely to believe in dreams and portents. Mercutio is not one to waste time on forebodings or being dreary. For example, in act 1, scene 4, Mercutio says that "That dreamers often lie" and that dreams are "the children of an idle brain":

Begot of nothing but vain fantasy,
Which is as thin of substance as the air
And more inconstant than the wind

In contrast, Romeo in act 1, scene 4 worries about a dream he had the night before that leaves him with a sense something bad is about to occur:

fear too early, for my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night’s revels, and expire the term
Of a despisèd life closed in my breast
By some vile forfeit of untimely death.

In sum, while the two friends have much in common, Romeo is dreamier, much more in love with love, and less prone to look for a fight for no reason. Mercutio is much more cynical and practical in general but especially about love. It is also worth noting that although vibrant and witty, Mercutio has a bit of mean streak that Romeo does not share. For example, near the end of act 2, scene 4, he can't resist insulting Juliet's nurse, implying she is a prostitute and truly getting under her skin. That kind of mean wordplay is not something the more earnest-hearted Romeo enjoys or indulges in.