I believe that two separate questions are being asked here. I think the first question asks for a brief character analysis of Mercutio based on this scene. I think the second question is asking for an example of dramatic irony in this scene.

When the scene begins, Mercutio and Benvolio are complaining of the heat, and Mercutio accuses Benvolio of being quick-tempered and always looking for a fight.

Thou art like one of those fellows that when he
enters the confines of a tavern claps me his sword
upon the table and says 'God send me no need of
thee!' and by the operation of the second cup draws
it on the drawer, when indeed there is no need.

These lines paint Mercutio as the calmer, more level-headed person; yet, moments later, we can see that Mercutio is just as hot tempered as Benvolio or Tybalt, or perhaps even more so. We are not told this. We have to infer it based on how quickly he starts antagonizing Tybalt into a brawl.

MERCUTIO

And but one word with one of us? couple it with
something; make it a word and a blow.

TYBALT

You shall find me apt enough to that, sir, an you
will give me occasion.

MERCUTIO

Could you not take some occasion without giving?

As for the dramatic irony of the scene, we have to wait until Romeo finally makes his appearance. Tybalt sees Romeo and immediately tries to pick a fight with him, but Romeo wants nothing to do with the fight. Romeo will claim that Tybalt doesn't know exactly who Romeo is, and Romeo will also claim that he loves Tybalt and the Capulet name. Tybalt has no idea what Romeo is blathering on about; however, audiences do know what Romeo means. This is a good example of dramatic irony in this scene, because we know something Tybalt and other characters do not know. We know that Romeo is now married to a Capulet; therefore, he seeks no quarrel with family.

TYBALT

Romeo, the hate I bear thee can afford
No better term than this,—thou art a villain.

ROMEO

Tybalt, the reason that I have to love thee
Doth much excuse the appertaining rage
To such a greeting: villain am I none;
Therefore farewell; I see thou know'st me not.

TYBALT

Boy, this shall not excuse the injuries
That thou hast done me; therefore turn and draw.

ROMEO

I do protest, I never injured thee,
But love thee better than thou canst devise,
Till thou shalt know the reason of my love:
And so, good Capulet,—which name I tender
As dearly as my own,—be satisfied.

In the Elizabethan time period, it was thought that a man too much in love is not actually a man at all, he is "effeminate".  In this scene, Romeo fights with his two selves - the more manly version that Mercutio knows who would fight at the drop of a hat and the softer version that Juliet knows who tries to keep the peace as he does not wish to fight with his new wife's kinsman.

There is a lot of debate on this subject, but it can be argued that Mercutio (his name means a mercurial nature) fights Tybalt on Romeo's behalf both to restore Romeo's manliness and because Tybalt essentially calls him bi or gay and says he's in love with Romeo.  It can be argued that this makes Mercutio especially angry because it's true.  The dramatic irony there would be that Mercutio fights Tybalt so Romeo doesn't look effeminate, but it is actually (according to Elizabethan sensibilities) Mercutio who is effeminate.