How does Shakespeare present Mercutio, Romeo and Tybalt in Scene 3 Act 1?
With a 3rd person narrative of each character, all we have to rely upon is the language in the dialogue to help us to understand how each character is presented. In the beginning of the scene, Benvolio is pleading with Mercutio to leave the public place because "For now, these hot days, is the mad blood stirring"(III.i.4); so I would say that Benvolio is presented as cautious.
Mercutio, on the other hand, seems defiant yet in a joking mood because he discounts Benvolio's warning; he even turns the issue back on Benvolio and says that he's worrying too much. The two friends are joking around with each other when Tybalt arrives seeking Romeo for a duel.
Tybalt is polite and formal with his greeting, but he is perturbed when Mercutio disrespectfully responds. Once Romeo appears on the scene, however, Tybalt stays his course to engage Romeo and ignores Mercutio. Tybalt is presented as a man on a fatal mission and refuses to steer from it.