I agree with #3.  He wants Zaroff to feel like he's being hunted.  Rainsford has now tracked him down and his him on an even playing field.  Zaroff is now the one who has to fight to stay alive.  Aside from this, I think an ambush would be pretty difficult.  Rainsford is unarmed and Zaroff is tucked away somewhere in his great chateau.  A sneak attack probably wouldn't be successful.

I agree with Aunt Lori. Rainsford was a sporting hunter, and it would not have been as satisfying to take unawares. There was probably a grim satisfaction for Rainsford when he stared Zaroff in the eyes and Zaroff new his most dangerous game was coming to an end, and this time he would be the loser.

All good points.  I'd only add that Rainsford is a hunter with some integrity--in other words, he would not be the guy who used unfair means to kill his prey (like some modern big cat hunters who, for example, shoot tigers and lions virtually undefended while held captive in their pens just to say they killed a wild cat).  He wanted to face his foe, give him the same fighting chance he would give any prey, make sure Zaroff knew it was him, and derive the satisfaction of knowing his enemy was aware of who killed him and why. 

Personally, I feel that Rainsford stops to have the breif discussion with Zaroff because he wants to make one very important point clear: He is not killing Zaroff as a man but as an animal.  Rainsford still believes that what Zaroff is doing is wrong.  He wants to clarify that he has not sunk to Zaroff's level by killing another man.  He wants to express the point that he is still an animal being hunted that is defending himself, not a man who is commiting murder.

That's a great question.  I think it comes down to the fact that every time a wrong is done, a crime is committed, people want to the know the "why".  Rainsford has suffered a horrible experience.  The fear and panic he felt must have been overwhelming.  Of course, he wants an answer where there probably is no answer...some psychopaths have no idea why they do what they do.  They only know they get a rush from being in power over someone else and causing pain. 

One gets the impression that this long short story might have originally been started by the author with the intention of turning it into a novel. There are many parts that could have easily been made into full chapters. The opening scene could make a chapter with the introduction of Whitney and Rainsford, their discussion of hunting, their discussion of Ship-Trap Island, and other exposition via dialogue. The chapter would end neatly with the following dialogue:

"I'm not sleepy," said Rainsford. "I'm going to smoke another pipe up on the afterdeck."

"Good night, then, Rainsford. See you at breakfast."

"Right. Good night, Whitney."

In the second chapter Rainsford would fall into the shark-infested Caribbean and swim to the island. In the third chapter he would find his way to the "palatial chateau" with great difficulty and knock at the door. That chapter would end with the bearded giant opening the door and pointing a long-barreled revolver at Rainsford's heart. A good ending for that chapter would be:

"Don't be alarmed," said Rainsford, with a smile which he which he hoped was disarming. "I'm no robber. I fell off a yacht, My name is Sanger Rainsford of New York City."

There is plenty of material for a short novel. It would take about five chapters of exposition and dialogue before the big chase had even begun. If Connell had written the story as a novel he would have given many thousands of words to the finale and described the deadly fight between Rainsford and Zaroff. He might have also devoted at least one full chapter to telling how Rainsford made it from one side of the cove to the chateau and into Zaroff's bedroom. But there is a big gap after this cliffhanger:

Rainsford hesitated. He heard the hounds. Then he leaped far out into the sea. . . .

It seems probable that Connell got tired of his plot and decided to end it quickly and submit it as a short story. When the motion picture adaptation was made in 1932, the big fight between Zaroff and Rainsford which seems to be conspicuous by its absence in the original story was written in by the screen writers and provides a more satisfactory ending that the cryptic line which ends Connell's tale:

He had never slept in a better bed, Rainsford decided.

"The Most Dangerous Game" is quite a long story for its genre. This is because so much space had to be used in the initial exposition. The author had to explain how Rainsford got to the island in the first place. Then he had to explain Zaroff's background, philosophy, and his hobby of killing humans for sport. Then there was the long chase, which is the main part of the story. The author may have felt that a description of some sort of fight between the two men would take up too much additional space. Their final battle is not described, but it is obvious that Rainsford won. It would seem that they had a duel with swords because Zaroff says, "On guard, Rainsford." Whatever weapons they used, Rainsford slept in Zaroff's bed that night.

In the film version of the story made in 1932, and available on  DVD, the two men have a violent battle in which the General tries to kill Rainsford with a powerful hunting bow but ends up mortally wounded and falling to be devoured by his voracious hunting dogs. This is the sort of battle Connell might have described in his story if he hadn't been concerned about length. Also, he might have figured that the more important contest was the one that took place outdoors when Zaroff was tracking Rainsford all over the island. Rainsford had already won their deadly game.

Please refer to the third link below for questions and answers regarding "Ending."

Rainsford is an honorable man who has only been sucked into Zaroff's game through the fateful events that surrounded his arrival on the island. Though Zaroff's game is one that involves murder, he, too, is a man of his word, and he plays the game according to the rules he has established. Rainsford's desire for revenge also seems to have overwhelmed the sense of fair play and humanity which he displayed earlier when he called Zaroff's human hunt an act of murder. Rainsford is not a murderer, and bushwacking Zaroff would be just that. Rainsford decides to allow Zaroff to play the game in order to give the Russian a taste of his own medicine because it is the only fair way for him to settle the score. And Rainsford may have actually taken to Zaroff's new game a little, and by playing it one more time, he will be able to find out for himself who the better man is. 

Why does Rainsford confront Zaroff instead of ambushing him in "The Most Dangerous Game"?

That's a good question.  There isn't any textual evidence that directly tells readers why Rainsford doesn't simply shoot Zaroff in the back from a concealed location.  I think one possible reason is pride.  Rainsford wants Zaroff to know that he has been beaten.  Rainsford also wants Zaroff to know that Rainsford beat him.  If Rainsford took a sneaky shot at Zaroff, Zaroff wouldn't know that he had been beaten by Rainsford.  Zaroff would just be dead.  Rainsford is a popular hunter.  His skills have made him famous, and he still finds hunting normal animals thrilling. On the other hand, Zaroff pompously claims that he has grown bored with hunting the most dangerous animals in the world.  In a way, Zaroff seems to be claiming that he is a far better hunter than Rainsford because animals are not a challenge anymore.  By showing himself, Rainsford essentially says, "See, I knew you weren't better than me."  

Perhaps another reason has nothing to do with pride.  Perhaps Rainsford simply wants Zaroff to know what it feels like to be the prey.  Rainsford has been hunted to within an inch of his life, and nothing was fun about it.  Zaroff thinks it is great fun because he is not the one being hunted.  Rainsford's motivation might be just wanting Zaroff to feel what it's like to have the tables turned.  

A third possible reason deals with Rainsford's general character.  Rainsford is a reasonably moral man.  Zaroff presents a fairly logical explanation as to why hunting humans is acceptable.  Rainsford isn't even intrigued in the slightest.  He's appalled from the very beginning, and he calls Zaroff a murderer.  

"Hunting? Great Guns, General Zaroff, what you speak of is murder."

I think Rainsford's morality just won't let him shoot a man in the back.  That's why he confronts Zaroff instead of ambushing him.  

In "The Most Dangerous Game," why does Rainsford confront Zaroff instead of ambushing him?

After his entrapment by General Zaroff, Sanger Rainsford begins to reassess his ideas about the hunter and the hunted. Whereas he has prievously told his friend Whitney that the hunted jaguar has no understanding of being their prey, after he is stalked by Ivan and the general, Rainsford comprehends that he now is the "mouse" and the Cossack is the "cat."  And,

[T]hen it was that Rainsford knew the full meaning of  terror.

Since he has now learned the terror of being "an animal at bay," Rainsford realizes that he will die if he does not escape; so, he dives far out in the waters of the sea from which he has been captured. Making his way successfully to the chateau, Rainsford is able to make his entry into Zaroff's bedroom.  He confronts the Cossak because he wishes to have the general face him in combat so that he will no longer be "a beast at bay," but a hunter again:

"I congratulate you ....You have won the game."
Rainsford did not smile.  "I am still a beast at bay....Get ready, General Zaroff."

For Zaroff, the hunt has, indeed, been a game.  He delights in identifying the traps, and like the cat that toys with the mouse, he lets Rainsford live one night and comes back the following day in order to continue the "game."  He, then, congratulates Rainsford on winning the game; however, Rainsford does not perceive Zaroff's hunt as any game since he considers himself "a beast at bay" who turns predator and kills his prey.

Why does Rainsford confront Zaroff instead of ambushing him?

These two men are professional hunters.  It is in the hunt that they take pride.  When Zaroff first tells Rainsford that he is to be hunted, Zaroff says,

"Your brain against mine. Your woodcraft against mine. Your strength and stamina against mine.  Outdoor chess! And the stake is not without value, eh?" (page 11)

If Rainsford simply ambushed him, he wouldn't get the satisfaction of letting Zaroff know that he had been beat at his own game.  Zaroff congratulates Rainsford in the end for winning the game.  However, it was necessary to kill Zaroff.  He wasn't about to let Rainsford off the island.  Rainsford knows this.  When Rainsford asked Zaroff what would happen if he wins, Zaroff tells him that he would be taken off the island, but he...

"....must agree to say nothing of your visit here" (pg 11)

Rainsford cannot agree to that.  After all, Zaroff is killing human beings!  When he tells Zaroff that he cannot agree, Zaroff says,

"Oh, in that case ----But why discuss that now? Three days hence we can discuss it over a bottle of Veuve Cliquot, unless...." (pg 11)

He leaves the ending open.  Rainsford wins the game, and he has to have the satisfaction of looking Zaroff in the eye and letting him know who won.  However, he knows he must kill Zaroff.  He tells him,

"I am still a beast at bay" (pg 15) (last page of story)

The term "at bay" refers to an animal that is cornered and is forced to turn and fight.  The reader has to respect Rainsford though.  He could have just shot Zaroff and finished him off.  Instead he challenges him to a dual with swords.  Again, the most talented of the two men will win.  Rainsford won.

What does Rainsford's choice to confront Zaroff reveal about his personality?

Rainsford is an old-fashioned sportsman. When he becomes the hunter rather than the hunted, he feels that he should show sportsmanlike conduct in dealing with his "prey." One of the rules of good sportsmanship is that the hunter should not try to avoid danger by any underhanded means. Ernest Hemingway had a lot to say about sportsmanship as applied to big-game hunting. His best-known works dealing with the subject are Green Hills of Africa, "The Short Happy Life of Francis Macomber," and "The Snows of Kilimanjaro." The only big-game hunters Hemingway admired were those who not only faced danger from wild animals but actually got a thrill out of risking their lives.

Ironically, Sanger Rainsford is much more akin to General Zaroff than he has previously thought as they dined together in the general's palatial chateau. Now, he, too, delights in "the most dangerous game" of hunting man. For, Rainsford has learned what his friend Whitney meant when he spoke of the desperate sense of fear of pain and death that the prey feel because he himself has been "a beast at bay" and felt terror. But, he returns to destroy his enemy.

Having escaped into the sea, Rainsford returns to the chateau and scales the rocks until he makes his way into Zaroff's bedroom where he confronts his adversary. Rather than wait until midnight of the next day when he would be placed upon the mainland near a town if not caught, according to Zaroff's agreement, Rainsford reverses the roles of hunter and huntee and kills his prey.

He had never slept in a better bed, Rainsford decided.

Indeed, Sanger Rainsford of New York has assumed the role of General Zaroff; he has resumed his role as the predator, and the game he has hunted is truly "the most dangerous."