at the ankle. "I mean, anybody can break through a screen door and glass and wood and iron or anything else if he needs to, anybody at all, and specially Arnold Friend. If the place got lit up with a fire, honey, you'd come runnin' out into my arms, right into my arms an' safe at home—like you knew I was your lover and'd stopped fooling around. I don't mind a nice shy girl but I don't like no fooling around."

Connie eventually offers herself as a sort of sacrifice to save her family, walking out of her house to meet her certain doom with Arnold Friend.

The internal conflict, Connie's ultimate insecurities with herself, allows Arnold Friend to sway her decisions to his advantage. She checks both mirrors and other people's faces to gauge her own. She knows that her mother prefers her meek older sister. She has a "high-pitched and nervous laugh" in public, unlike the one she uses at home. Connie chases boys and lies about where she is, trying to fill some void in herself through the approval of others. Arnold uses this to his advantage, telling her,

"The place where you came from ain't there any more, and where you had in mind to go is cancelled out. This place you are now—inside your daddy's house—is nothing but a cardboard box I can knock down any time. You know that and always did know it. You hear me?"

Arnold erodes Connie's sense of family and safety by ultimately conveying that she doesn't belong in her family, which is a reflection of her internal conflict. This drives Connie to detach from her own body and submit to Arnold's desires:

She felt her pounding heart. Her hand seemed to enclose it. She thought for the first time in her life that it was nothing that was hers, that belonged to her, but just a pounding, living thing inside this body that wasn't really hers either.

Arnold Friend is able to recognize Connie's internal conflict and then use it for his own malevolent purposes, driving the external conflict which ends Connie's life.

There are several conflicts in Joyce Carol Oates's disturbing story, "Where Are You Going, Where Have You Been?"

EXTERNAL CONFLICTS

• Connie conflicts with her mother, who finds Connie vain, sloppy, and cheap. She scolds Connie for not keeping her room clean.
• Connie has "...two sides to it [her personality], one for home and one for anywhere that was not home." For example, Connie has one laugh at home, which is "cynical and drawling." This laugh causes friction with her mother. She has another laugh when she is out, which is "high-pitched and nervous"; this is the laugh she uses with boys.
• Connie becomes so weary of her mother's criticisms that she sometimes wishes that her mother were dead and that "she herself were dead and it was over."

"...the two of them kept up a pretense of exasperation, a sense that they were tugging and struggling over something of little value to either of them."

• One Sunday Connie refuses to join her family at her aunt's barbecue.
• When Arnold Friend later arrives, he tells Connie that she will come with him. "I want you," he tells her.
• Later, Arnold frightens Connie into coming outside because he threatens to harm her family: "You don't want them to get hurt."

INTERNAL CONFLICTS

• Connie's mind is so filled with cluttered thoughts that she cannot find the time to clean her room, much to the exasperation of her mother. 
• As she lies in the sun, Connie daydreams with carnal images. However, she grows too hot as she lies in the sun. So she goes indoors; there she turns on the radio in order "to drown out the quiet." 
• When Arnold Friend arrives, Connie experiences her first serious anxiety: "She spoke sullenly, careful to show no interest or pleasure." 
• As she looks at Arnold Friend's car, Connie becomes more worried.
• Connie becomes anxious about Arnold, wondering who he is, and she is frightened by his explicit sexual language.
• He tells Connie that she must come with him or her family will get hurt. "Don't you know who I am?" he asks, and Connie becomes terrified.
• Connie grows sick with fear. She tries to scream into the telephone and cries for her mother. 
• Connie has a sick premonition as Arnold induces her to come outside. "She was hollow with what had been fear, but what was now just an emptiness." She worries that she will never see her mother again. 
• Connie opens the screen door, and as she rides in Arnold's car, a terrified Connie does not recognize where she is going, but she knows that she is headed for this unknown place.

One of the conflicts present in the story is that between the real world in which Connie lives and the daydream fantasy world she'd much prefer to inhabit.

On the whole, it's fair to say that the real world doesn't do Connie too many favors. For one thing, she's constantly at odds with her mother, who's forever criticizing her for every little thing. To make matters worse, Connie's mother always makes unflattering comparisons between Connie and her sister, June.

Given the situation she finds herself in, it should come as no surprise that Connie should spend a lot of her time having what her mother describes as “trashy daydreams.” Ironically, it's largely because of her mother's constant disparagement of her, her constantly putting her down, that Connie has these daydreams in the first place.

As she's unable to maintain an appropriate balance between the worlds of reality and fantasy, Connie finds herself vulnerable to the overtures of the inappropriately-named Arnold Friend. By getting into the car of this strange young man, Connie is putting as much distance as possible between herself and her home life, with all its challenges. For now, at least, the fantasy world that she often inhabits—and to which she often retreats—has taken over.

The first conflict readers encounter in “Where Are You Going, Where Have You Been” is between Connie and her mother and sister. Connie’s older sister, June, is described as “plain and chunky and steady.” She makes decisions that her mother approves of, and this is in stark contrast to Connie, who her mother considers to be focused on her “trashy daydreams.” The seriousness of this family conflict is summed up nicely as follows:

Connie’s mother kept picking at her until Connie wished her mother was dead and she herself was dead and it was all over.

As is the case with many teenage girls, Connie is going through a phase of experimentation and finding new ways to express herself. Many of her words and actions do not fit into her mother’s image of who her daughter should be, and this causes conflict.

Serious as this conflict may seem, Connie becomes embroiled in a far more serious conflict later on. Having attracted the attention of a lowlife “with shaggy black hair,” Connie is home alone one afternoon while the rest of her family has gone to a barbecue, which Connie chose not to attend. A car pulls up, and the man with the shaggy hair has arrived, together with another man. Connie becomes intimidated when she realizes that this “boy” knows a lot about her that she has not told him. With a shock, she realizes that he is not a boy, but an older man. She instructs him to leave. When he refuses, she realizes that she is in a dangerous situation and runs inside. The conflict escalates further when he threatens to hurt Connie’s family if she does not comply with their wishes.

Unlike in the conflicts with her mother, Connie surrenders in this instance. The conflict is “resolved” when she acquiesces to his demands and comes back outside to an unknown future.

The most evident conflict in the Oates short story exists between Arnold Friend and Connie.  This does not start out as conflict.  Rather, it is one where her desire for attention and notoriety has been reciprocated by Arnold.  The conflict emerges when Arnold becomes so emboldened with his advance towards Connie.  His desire to have her come with him and, eventually, kidnapping her becomes the basis of the conflict.  He uses psychological and physical manipulation in his attempt.  From this, Connie recognizes that she does not want to go with him, but also grasps that she has little choice, as Arnold Friend threatens her family and leaves her with little choice.  Arnold demonstrates some slight conflict internally between his age and his desire to appear young, allowing him to get close enough to lure girls like Connie.  This conflict comes out in different points, such as when he speaks in different vernaculars of youth, but overall, he has little problem in being the person who stalks and victimizes Connie.

This development of Connie's character as one who cares for her family is one that is not present at the start of the story.  Connie is first shown to be in conflict with her parents and her sister.  Connie seems them as too traditional and unable to fully understand her own predicament and her need to be independent from them.  Connie's conflict with her sister is that she is too "plain," and unable to grasp the need to be "hip" and popular.  In the end, Connie's conflicts at the start of the story vastly contrast with her conflicts at the end of it.

I am not allowed to write an essay for you, but I believe that I can get you on the right track by answering several of the questions in the prompt.  

There are several conflicts in "Where Are You Going, Where Have You Been?" It's going to be up to you to decide which one you think is most "central."  There is a conflict between Connie and her parents.  She desires to be more independent, and she also sees them as too traditional.  There is also a conflict that exists between Connie and her sister, June.  It's not a huge conflict, and I'm not certain that June is even aware of it.  The conflict is that Connie has a problem with how "plain and steady" June is.  Connie doesn't understand how June doesn't desire to be more flirty and cool.  I don't believe that either of those conflicts are the central conflict.  For the central conflict, I would definitely write about the conflict that develops between Connie and Arnold Friend. 

The question asks about the nature of the conflict and how it changes.  I believe that those two questions come together.  When Connie first sees Friend, there's very little conflict to speak of.  He creepily says "Gonna get you, baby," but Connie just keeps walking.  The encounter seems to be over and done with. 

It's not until a few days later that the conflict between Connie and Friend becomes extremely serious.  Readers are told that Friend shows up at Connie's house near midday on a Sunday.  Connie opens the door to see who it is, and Friend immediately begins trying to convince her to get in his car and go for a ride. 

"You wanta come for a ride?" he said.

Connie smirked and let her hair fall loose over one shoulder.

"Don'tcha like my car? New paint job," he said. "Hey."

"What?"

"You're cute."

At first, Friend's tactics resemble confident flirting; however, as Connie continues to fend off his advances, Friend becomes threatening.  His threats are a combination of psychological and physical manipulation.  He knows things about Connie and her family that he just shouldn't know.  He knows exactly where her family is and how long they are likely to be gone.  

"But my father's coming back. He's coming to get me. I had to wash my hair first—'' She spoke in a dry, rapid voice, hardly raising it for him to hear.

"No, your daddy is not coming and yes, you had to wash your hair and you washed it for me."

Eventually, it becomes clear to Connie that Friend is really bad news.  He threatens to physically come in the house after her if she attempts to call the police.  By this point, Connie is so scared that she decides to risk rushing for the phone.  Friend comes in the house as he threatened to do, and he stabs her "again and again with no tenderness."  She's not being stabbed with a knife or anything like that, and critics have various opinions on what is actually happening to Connie; however, the result is still the same.  Connie leaves the house with Friend, and she is unable to fight any longer.  She's a complete shell either because she's so scared or because she has given up.  

The final part of your question asks about the conflict's resolution.  The conflict is resolved when Friend wins.  Connie leaves her house thinking that she will never see her family again.  

She thought, I'm not going to see my mother again. She thought, I'm not going to sleep in my bed again.

This story is one of those rare times that the "bad guy" wins.  In my opinion, the resolution is not satisfying.  Perhaps it is more realistic than the ever-present happy ending conflict resolution, but happy endings are satisfying to me.  I love teaching this story to classes because students are upset at the ending.  They are not happy that the story doesn't have a clean, happy, and satisfying conflict resolution.  

This is an interesting question, and one could easily argue that there are really two central conflicts: the internal ones that rage within Connie herself, and the one between Connie and Arnold when he shows up at her house. These are the opposing conflicts in Oates's story.

Connie's internal conflicts are centered on her desire to be noticed and valued for her beauty, even when that means breaking rules, defying her parents, and exemplifying the opposite of her sister June who is "plain and steady." The narrator describes Connie as having a dual, conflicting nature: "Everything about her had two sides to it, one for home and one for anywhere that was not home."  While she is at first flattered by Arnold Friend's attention, his interest in her becomes a serious problem.

While Connie's internal conflict is not at all unusual or potentially catastrophic in a fifteen-year-old girl, the conflict in which she becomes enmeshed with Arnold Friend is quite dangerous.  He is a predatory adult male with naive, vain Connie in his sights.  She is no match for his determination to have her, and at the moment he strikes, no one is available to help her. Ultimately, she is unable to help herself.  Readers are left to assume that the conflict ends badly for Connie.