What are five conflicts in chapters 1 to 15 of Huckleberry Finn?

Conflicts are a way for characters to make decisions and prove themselves and also a way for the plot to move forward, sometimes unpredictably. In The Adventures of Huckleberry Finn, characters face a string of conflicts, many of which are quickly resolved. In chapters 1–15, five conflicts include:

Huck vs. Religion in chapters 1–2

Huck is living with two spinsters, and although he has money in the bank (thanks to the town judge managing the money he and Tom found in Twain's previous story, Tom Sawyer), is getting an education, and is wearing good clothes, he chafes at it. He especially hates religion and sees no use in prayers. All of these things represent civilization, but it's fair to say Huck has an especially low regard for religion as something useless and impractical.

Huck vs. Himself in chapters 3–4

He is beginning to get used to schooling and get into the rhythm of his new life, but Huck still feels the pull of the past and has feelings of concern over whether his father will show up again. He isn't completely sure where he fits in due to all the changes to his daily life. His self-doubt portends a dark and difficult next few chapters.

Huck vs. Childhood in chapters 4–7 & Huck vs Pap in chapters 4–7

Huck's father reappears in the story, despite rumors that he is dead. He is a mean and controlling man, and Huck has mixed feelings about him. He dislikes him, but Pap is his only family. The conflict with Pap continues as Huck learns that Pap mainly wants his money, then Pap essentially holds Huck hostage in his cabin. Huck escapes by pointing a gun at his father and leaving by raft. He narrowly misses his Pap, who is out looking for him in the darkness while they are both on the river. In these chapters, Huck must fight his father, and the conflict is obvious. Huck is also in conflict with his past and childhood, as he steps up to confront the abuse and decides to leave. He tries to make it appear that his Pap is dead, so others will think that Huck no longer has a father to command him.

Huck vs Jim in chapter 15

In chapter 15, Jim and Huck are traveling down the river looking for the city of Cairo. A fog descends upon them. This separates them (which could be interpreted as conflict with nature), and in the confusion Huck plays a trick on Jim. Like the first trick in chapter 10, when Huck put a dead snake on the sleeping Jim which proved to be alive and bit him—it backfires. This time, Jim becomes angry and Huck feels ashamed of what he's done. He realizes how much he likes Jim and how much he needs him. This is an important conflict because Huck begins to show more maturity. It's their first real argument and is a conflict that marks a turning point in their relationship.

What are some conflicts in the first 15 chapters of The Adventures of Huckleberry Finn?

Fifteen chapters of Huckleberry Finn is a lot of novel and many "conflicts" so I will only add a few to supplement the excellent answers already provided.  

One important conflict is symbolized by the contrast between the Widow Douglass and her sister, Miss Watson, who represent two types of Christians. The widow is a sort of idealized Christian who does good works and is full of Love: In many ways she represents the better side of our current philosophies, the ones which emphasize Jesus's moral and loving message and downplay the Hell-fire and damnation side of the equation.  Miss Watson is the opposite.  She represents a sort of holier-than-thou Christian (or any religious person) who believes that he or she is living in line with the rules of proper Christian behavior and that everyone else who is not doing the same is a sinner in God's eyes and is going to suffer eternal punishment in Hell after this life.  

Sometimes the widow would take me one side and talk about Providence in a way to make a body's mouth water; but maybe next day Miss Watson would take hold and knock it all down again. I judged I could see that there was two Providences, and a poor chap would stand considerable show with the widow's Providence, but if Miss Watson's got him there warn't no help for him any more.  (Chapter 3)

A very revealing conflict of sorts is revealed in the very next sentence where Huck concludes that he would be willing to "belong" to the widow's Providence "if he [God] wanted me" even though he can't understand why God would want an "ignorant" as well as "low-down and ornery" fellow like himself.  This conflict is perhaps a form of man vs. himself, for Huck, who is with the possible exception of Jim about the most moral person in the book, thinks of himself the way society sees his family, as white trash.  This belief that other people, people who are better educated, or go to school, or church, or hold jobs etc. are better people, and that God approves of such people and disapproves of people like Huck, well, that idea is at the base of the largest conflicts in the book.  After all, we must remind ourselves, that all the so called good, church-going, proper, moral, upright people in the novel, for the most part, either own slaves or approve of the institution of slavery.  For example, late in the novel, Tom Sawyer offers to help Huck in his effort to free Jim.  Well, Huck simply cannot understand this: To Huck, Tom is a good boy who should not be involved in such a seriously evil (in Huck's perception, which has been warped by his society) act as helping a slave escape: 

Well, one thing was dead sure; and that was, that Tom Sawyer was in earnest and was actuly going to help steal that nigger out of slavery.  that was the thing that was too many for me.  Here was a boy that was respectable, and well brung up, and had a character to lose; and folks at home that had characters; and he was bright and not leather-headed; and knowing and not ignorant; and not mean, but kind; and yet here he was, without any more pride, or rightness, or feeling, than to stoop to this business, and make himself a shame, and his family a shame, before everybody. I couldn't understand it, no way at all.  It was outrageous...   (Chapter 34)

This passage reveals so much of what makes Huckleberry Finn the great American classic that it is.  Huck's sincerity and genuine good feeling, indeed love, in wishing to free Jim from slavery is the most moral and upright thing in the novel--yet he sees himself, and his plan to free Jim, as the exact opposite of that, as dirty, low, immoral, shameful, literally disgusting!  This is Twain's ingenious indictment of the Southern Society he was raised in--that it taught everyone who wanted to live in that society as an accepted member of the social world that slavery was good, and that those who opposed slavery or aided slaves in escaping, were evil--when Twain could see and wanted his readers to see that the exact opposite was true: That slavery was evil and that those who opposed it or aided slaves in escaping were good!  This conflict, that Southern Society was teaching that what we know  to be evil (slavery) was good, and what we know to be good (undermining slavery) was evil is the true heart of this amazing novel.  It creates the single greatest conflict in the novel, Huck versus himself, because Huck's natural goodness knows that the right thing to do is to set Jim free, but his conscience, which would normally tell a person what is right or wrong, has been warped by his Southern upbringing so horribly that he feels guilty for helping Jim!  Thus, in the greatest chapter in the novel, Chapter 31, when Huck decides he will literally go to Hell if that is the price he must pay for helping his friend, we should remind ourselves that Huck has been raised among church-going, strict Baptists for whom Hell is a real and terrible place--eternal damnation--eternal suffering and torture--a place where one burns forever!  How tragic, that a good boy, doing the right thing, should be made to feel that he is evil and degenerate for actions that are objectively moral!

In the first fifteen chapters, the author sets up many of the conflicts that will appear again and again in the novel. Perhaps the most important conflict we see is man vs. society. Huck Finn is being “sivilized” and he is not sure if he likes it or not. For example, he likes going to school and learning, but he is told by his Pap learning is worthless. “And looky here, you drop that school…” Huck enjoys being warm and dry, but he does not enjoy the rules that go along with living in the widow’s house. “I liked the old ways best, but I was getting so I liked the new ones, too, a little bit.”

The man vs. society conflict can also be seen in the game of robbers, the brain child of Tom Sawyer. The elaborate game shows a desire to go against the rules of society, yet at the end of the chapter, the boys decide it would be “wicked to do it on a Sunday.”

Another place the reader can see the man vs. society conflict is in Huck’s reaction to meeting Jim on the island. Huck is startled by Jim’s revelation that he has run off, but he promises not to turn Jim in, even though society views that decision as wrong. “People would call me a low-down Abolitionist and despise me for keeping mum, but that don’t make no difference.” Huck knows society would not approve of his decision, but he makes it anyway. In the first fifteen chapters, one can also see the internal (man vs. himself) conflict Huck is facing. Huck wants to do the “right thing,” but he is unsure if the right thing is what society tells him or what his heart tells him.

After Huck plays a trick on Jim, making him doubt himself, Jim scolds Huck. Huck knows he has done something wrong. “It was fifteen minutes before I could work myself up to go and humble myself to a nigger, but I done it, and I warn’t ever sorry for it afterward.” This sets up the internal conflict for the rest of the novel: is Jim property or is he a person?

Another conflict occurs when Huck and Jim stumble across a wrecked steam boat during a storm in chapter 12. The first external conflict in this scene is the physical storm that is creating chaos for boats and rafts on the river. Next, Huck and Jim disagree about whether or not they should explore the wreck. Their disagreement is another external conflict. Huck wonders if they might be able to find any valuables that people left behind. Jim, however, imagines that someone will be on board to keep watch over the wrecked ship who might make trouble for them:

"I doan' want to go fool'n 'long er no wrack. . . . Like as not dey’s a watchman on dat wrack." "Watchman your grandmother," I says; "there ain't nothing to watch but the texas and the pilot-house; and do you reckon anybody's going to resk his life . . . when it's likely to break up and wash off down the river any minute?"

Eventually, they agree to explore the boat. When they get on board, they overhear three robbers having an argument. Two of the criminals are threatening to shoot the third criminal to cover up one of their crimes. The endangered man cries out,

Oh, please don't, Bill; I hain't ever goin' to tell.

Huck and Jim have to decide how they will act towards these men; this is an internal conflict in the scene. The other two robbers eventually agree that they will leave the third man to drown with the sinking boat (instead of shooting him.) After, Huck makes a decision about how to respond. He tells Jim that they should try to stop these criminals from escaping:

Quick, Jim, . . . ; there's a gang of murderers in yonder, and if we don’t hunt up their boat and set her drifting down the river so these fellows can’t get away from the wreck there’s one of ’em going to be in a bad fix. But if we find their boat we can put all of 'em in a bad fix—for the sheriff'll get 'em.

Huck wants to leave all three of the robbers stuck on the boat so that a sheriff can find all three men. Unfortunately, Huck and Jim encounter another conflict when they realize that their raft has floated away (yet another external conflict). Jim, scared to be left alone with the criminals, cries out

Oh, my lordy, lordy! raf"’? Dey ain' no raf' no mo'; she done broke loose en gone I—en here we is!

Huck and Jim find the criminal's boat and float away on it when the robbers aren't looking. As they go away, Huck faces continued internal conflict as he decides whether or not he should send someone back to help the three men trapped on the sinking steamboat:

Now was the first time that I begun to worry about the men—I reckon I hadn’t had time to before. I begun to think how dreadful it was, even for murderers, to be in such a fix. I says to myself, there ain’t no telling but I might come to be a murderer myself yet, and then how would I like it?

Huck, feeling bad for the robbers, stops on shore to tell someone that there are people on the boat. He makes up a story full of lies about who the people are, but he tells these lies to convince people to help the robbers.

Chapters 12 and 13 are filled with both internal and external conflicts as Huck and Jim explore a sinking steamboat.

The most significant conflict from the first fifteen chapters is the one that pits Huck against his father. Huck is abused, verbally and physically, by his drunken father, Pap Finn.

Pap wants to take over the upbringing of his son and find a way to get Huck's money. Huck is endangered by his father and so must escape from him. 

This external conflict leads Huck to devise a plan to fake his own death and head down the river. 

An internal conflict that appears in these early chapters relates to Huck's moral dilemma. When Huck meets Jim on the island and hears Jim's story, he realizes that he is going to have to choose sides. He wil either side with Jim, keeping his secret and helping his run away, or he will side with "society", agreeing with its laws and morals and turning Jim in. 

Huck is divided about what the right thing to do is in this situation. He chooses to side with Jim but remains conflicted.