In "Raymond's Run" by Toni Cade Bambara, what conflicts does Squeaky face?

It is an interesting idea to think about Squeaky, in Toni Cade Bambara's "Raymond's Run," having much of any conflict because she is so self-confident and strong. She does have several, however. 

She is in conflict with her peers for several reasons because she does not think like most of them do. First, she does not see her mentally challenged brother as something to be made fun of like at least some of her classmates (and other people in town) do. He is her brother and she is determined to protect him from the dangers of just walking down the street as well as from unkind people.

Second, she thinks differently than others about things. While others are not too interested in working hard to achieve their goals, Squeaky works hard and does not mind that everyone else knows it.

Now some people like to act like things come easy to them, won’t let on that they practice. Not me. I’ll high-prance down 34th Street like a rodeo pony to keep my knees strong....

While others enjoy dressing up and showing off their finest clothing (which Squeaky sees as a waste of good money) or prancing around in a ridiculous costume, Squeaky is more concerned about being a decent human being. The last line of the story is a good reminder that too many of the girls she knows are

too busy being flowers or fairies or strawberries instead of something honest and worthy of respect . . . you know . . . like being people.

Squeaky is in direct conflict with Gretchen because they both intend to win the race. Squeaky says Gretchen  

has put out the tale that she is going to win the first-place medal this year. Ridiculous.

One conflict which is both internal and external is with Mr. Pearson. He intends to write her name down on his clipboard just as he knows her (which is not an outrageous thing for him to do); however, Squeaky chooses this moment to demonstrate her independence, as well as her individuality and personhood, by insisting he write down her full name: 

“Hazel Elizabeth Deborah Parker,” I correct him and tell him to write it down on his board. 

Squeaky also has a bit of an internal conflict when she decides that she could trade running, the thing that has been all-consuming for her, for training Raymond to run; however, it is rather an easy thing for her to decide. She may not do it, but she is willing.

In short, Squeaky knows what is important to her and is not afraid to show it. This attribute often puts her in conflict with others, but it is the kind of conflict she embraces. 

In "Raymond's Run" by Toni Cade Bambara, provide two examples that illustrate Squeaky's worldview.

Hazel Elizabeth Deborah Parker, better known as Squeaky, is the protagonist of Toni Cade Bambara's short story "Raymond's Run," and she is a young lady who knows what she wants. 

From the first lines of the story, we know that Squeaky is different than the other girls because she does not have to spend her time on chores like they do. That is probably because she has an older brother who is mentally challenged, and it is clear that she spends a lot of time with him. We also know she spends a lot of time training to run rather than doing silly or foolish things like the other girls her age, and it is her attitude about Raymond and about herself which most reveal how Squeaky views the world.

Raymond is 

subject to fits of fantasy and starts thinking he’s a circus performer and that the curb is a tightrope strung high in the air. And sometimes after a rain he likes to step down off his tightrope right into the gutter and slosh around getting his shoes and cuffs wet. 

Despite her brother's unusual behavior, Squeaky is very matter-of-fact as she deals with him and very protective of him when others try to make fun of him. 

One day she and Raymond are walking when they are stopped by several of Squeaky's classmates. Though they smile and make small talk for a moment, it is clear the girls are not friends and their intentions are anything but friendly. One of the girls starts this conversation, trying to goad Raymond into talking so she can make fun of him:

“What grade you in now, Raymond?” 

“You got anything to say to my brother, you say it to me, Mary Louise Williams of Raggedy Town, Baltimore.” 

“What are you, his mother?” sasses Rosie. 

“That’s right, Fatso. And the next word out of anybody and I’ll be their mother too.”

This bit of dialogue represents exactly how Squeaky views her world: it is her job to protect Raymond and she intends to do it. Anyone who tries to make fun of him is going to have to deal with her, and she wants to make sure the experience is an unpleasant one--for the other person, anyway.

We also have many, many examples of Squeaky's self confidence, claiming that she is the best and the fastest runner, that she does not care if everyone knows she wants to win and is willing to work hard to do it, and that she has no time for the foolishness she sees in the other girls. It is a bit arrogant-sounding, but she is the fastest runner and she does work hard and the other girls are a bit foolish, so we will call it confidence.

One other apt piece of dialogue happens when Squeaky goes to sign up for the race. She does not arrive all dressed up, like the other girls, and go

out there prancing around a May Pole getting the new clothes all dirty and sweaty and trying to act like a fairy or a flower or whatever you’re supposed to be when you should be trying to be yourself.

Instead, she shows up just for the race, settles Raymond into the swings, and concentrates on the race. When Mr. Pearson comes to record her name, "Squeaky," on his clipboard, she says,

“Hazel Elizabeth Deborah Parker,” I correct him and tell him to write it down on his board. 

This quote speaks to her determination to be herself, not someone others want her to be. We see several other examples of this, but this one is a short, powerful assertion of her independence and identity. 

Please give two examples of dialog or behavior that show how Raymond from "Raymond's Run" by Toni Cade Bambara views the world. Cite the page and line numbers of each example. 

Unfortunately, you asked two separate questions, so I had to edit out the second. Please feel free to re-post it as a second question. Listing page numbers and lines will not be very helpful, I fear, because I have no way of knowing in what anthology you are reading this story.

Raymond is an essential character in Toni Cade Bambara's "Raymond's Run. (We know that, of course, because this story is called "Raymond's Run" though it is actually about his sister's running, in terms of plot.) Raymond is the mentally challenged brother of Miss Hazel Elizabeth Deborah Parker. It would be pretty difficult to find several lines of dialogue for him since he never speaks, so perhaps that is one excellent example of how Raymond views the world. He does not join it: he simply looks and listens. Even when one of the girls in Hazel's class try to goad him into conversation, Raymond does not speak. His sister does the talking for him.

A second example of how Raymond views the world is seen in his climbing the fence after Hazel ran (and won) the race. Again he does not speak, but Hazel hears him, nevertheless.

Then I hear Raymond yanking at the fence to call me and I wave to shush him, but he keeps rattling the fence like a gorilla in a cage like in them gorilla movies.

This image, of a young man being trapped in a cage, is apt for Raymond. His limitations have him trapped, and he must surely feel as if he is caged in a world with which he has so little in common. He is generally happy, though, so perhaps he sees the world more like it is--the "cage" is really just a fence (barrier), not a cage. 

The good news in this story is that Hazel not only protects him, and certainly has the ability to do it effectively, but she also recognizes that he has the potential to break out of that cage (or out from behind the fence) as a runner and is willing to teach him. Until that happens, though, Raymond lives in a silent, rather caged (shut-off) world.