How do Benvolio's actions change Romeo's way of thinking in the first scenes and what are Benvolio's desires, obstacles, actions and thoughts?

As his name suggests, Shakespeare wants the audience to see Benvolio as good, a peacemaker and a pragmatic character, in contrast to the dreamy Romeo and the volatile Mercutio. Benvolio attempts to be a good friend and cousin to Romeo in the beginning of the play as he discusses Romeo's depression over his unrequited love for Rosaline. Benvolio doesn't believe Romeo should focus so much on just one woman. He urges Romeo to look at other women:

By giving liberty unto thine eyes.
Examine other beauties.

Benvolio has a common sense approach to Romeo's problem. He knows that all Romeo needs is to find another woman. His biggest obstacle in convincing Romeo is his cousin's mostly melancholy attitude about any of his suggestions.

When the two men come across the illiterate servant in the street they find out that Rosaline will be at the party and Benvolio convinces Romeo that they should attend so he can show off other women who might be to Romeo's liking:

At this same ancient feast of Capulet’s
Sups the fair Rosaline whom thou so loves,
With all the admirèd beauties of Verona.
Go thither, and with unattainted eye
Compare her face with some that I shall show,
And I will make thee think thy swan a crow.

In Act I, Scene 4 as the Montague men are on their way to the party, Benvolio expresses his desire to simply have a good time and enjoy the dancing:

Come, knock and enter, and no sooner in
But every man betake him to his legs.

Romeo is mostly unreceptive to Benvolio's ideas. He is still gloomy and depressed. He refuses to dance, suggesting he is too heavy hearted over Rosaline and really won't be able to enjoy himself:

Not I, believe me. You have dancing shoes
With nimble soles. I have a soul of lead
So stakes me to the ground I cannot move.

In Act V, Scene 5, however, because of Benvolio's advice (they wouldn't have been at the party if it hadn't been for Benvolio), Romeo does see another beauty and uses almost the exact same language as Benvolio had used earlier when he first sees Juliet across the room:

Beauty too rich for use, for Earth too dear.
So shows a snowy dove trooping with crows

Romeo simply replaces swan with dove, but it is the same idea. It is an obvious nod to his loyal friend and cousin who has advised him well. Romeo instantly forgets Rosaline and "that name's woe" once he finds Juliet. That Benvolio never knew how much his counsel helped Romeo is unfortunate.