How does the narrator's age (16) affect the purpose of the story "The Triumph of the Egg"? Use TE to help explain your answer. What positive human qualities does the boy associate with horses? Explain using TE. How does the story's setting help to reveal important plot points? Is the boy a hero or an anti-hero? Explain, using TE. When the boy discovers "the truth" about Tillford at the window, does he discover the evils in the world or is the narrator simply naive and in denial about the realities of the world? Use TE to explain yourself. What is the story's theme? Use TE to explain your answer. What literary elements can be used in Anderson's story? Explain.

You've asked quite a few questions here, so let's progress methodically through them.
The unnamed narrator's age is significant because of the chronology of the events that occur within the story. At the beginning of the tale, the boy is sixteen years old; however, when the events that he describes within the narrative occur, he is fifteen. The space of the calendar year (approximately) that has transpired since the incident allows the narrator to think excessively about it. In fact, he comments, "I did and saw that alone. That's what I'm writing about. It got me upset. I think about it at night," insisting that still, after all this time, he "wants to know why." His age also renders the story thematically significant because it depicts the boy's confusing sexual awakening. Although the boy is at an age where he would be beginning to understand his sexual identity, he doesn't have this sort of crystalline perspective; rather, he merely understands that he has lost his boyhood innocence and is moving into manhood, commenting, "I’m getting to be a man and want to think straight and be O.K."
The boy associates horses with many human characteristics. He refers to them as "beautiful" and states, "There isn't anything so lovely and clean and full of spunk and honest and everything as some race horses." He also compares Sunstreak, the stallion that wins the race, to a "girl you think about sometimes but never see," and says that "when you look at this head you want to kiss him." 
The story's setting is significant in that it shifts. The boy is from Beckersville, Kentucky, but hops a train to Saratoga, New York, to watch the race. This movement from the rural country setting to a larger city where he can finally watch a "first-class" race suggests that some sort of transformation is about to occur; this new city also offers a vaguely threatening sense of the foreign to the uninitiated. The narrator comments that this is thrilling:

But about Saratoga. We was there six days and not a soul from home seen us and everything came off just as we wanted it to, fine weather and horses and races and all.

I would argue that the boy is a hero rather than an anti-hero because he is in possession of the typical qualities of a traditional hero: idealism, a sense of morality, and so on. The boy is so angered by Jerry's involvement with the prostitutes after the race that he says, "Sometimes I'm so mad about it I want to fight someone." He is firmly committed to his love for horses and for racing, albeit in odd and unique ways; it is his "cause."
When the boy encounters Tillford at the window, he comments, "It's what give me the fantods. I can't make it out." He sees the prostitutes, who he describes as "ugly mean-looking women, not nice to look at or be near," yet he never actually identifies them as prostitutes. Rather, he just refers to them as "bad women." This suggests that he has indeed discovered the evils of the world but that he is too naive to understand what they are while still able to discern that they are, indeed, evil. He doesn't know that Tillford is engaging with prostitutes, but he does know how it makes him feel:

I began to hate that man. I wanted to scream and rush in the room and kill him. I never had such a feeling before. I was so mad clean through that I cried and my fists were doubled up so my finger nails cut my hands.

Thematically, we can see that the story deals with sexual awakening and the confusion that surrounds it. Because the boy is too naive to recognize what is happening within him, he subverts and sublimates his desires toward racing and the horses. This is why his descriptions seem almost sexual in nature and why he humanizes the horses (see the above quote regarding the horse as being like a girl). The boy is not able to identify his burgeoning sexual feelings, so he ascribes this passion to his love for horses. When he sees that Tillford possesses both a love for horses and a lust for women, he is disturbed: 

It's because a man like Jerry Tillford, who knows what he does, could see a horse like Sunstreak run, and kiss a woman like that the same day. 

In terms of literary elements, Anderson uses a great deal of sensory imagery to flesh out the narrative, like when he describes what it's like to be at the stables:

Well, out of the stables they come and the boys are on their backs and it's lovely to be there. You hunch down on top of the fence and itch inside you. Over in the sheds the niggers giggle and sing. Bacon is being fried and coffee made. Everything smells lovely. Nothing smells better than coffee and manure and horses and niggers and bacon frying and pipes being smoked out of doors on a morning like that. It just gets you, that's what it does.

He also uses hyperbole to indicate the depths of the boy's passion ("When I was ten years old and saw I was growing to be big and couldn't be a rider I was so sorry I nearly died") and similes ("I can pick them nearly every time. It's in my blood like in the blood of race track niggers and trainers").