Great base with potential
First off, I'm sorry it took me so long to review, but here I am! From the few chapters that are up, you get a pretty clear picture of what the story is about and what it promises. I like the concept of the story a lot, I've actually been thinking of writing a story for a similar idea, with a contest to decide the next ruler and such. (tho that story won't be coming anytime soon, not until I finish one of my current stories) It's really interesting to see how someone with a similar concept can still turn it into something so different. So yeah, it was an interesting read for sure.
Read the story now
Now, there are a few things I personally think you could improve on. From what I've read of other reviews they mention the pacing often, and although it has already been said, I'd still like to give my thoughts on it. The pacing is rather fast, but I know a few tricks that might help you out showing it. Whenever you write a scene, don't try to tell what is going on as if it was depicted in a movie or tv show. Instead, try really picturing the entire scene you are writing at that moment before moving on to the next scene. What is happening? Where are the characters? What is important? What does this scene accomplish? Why is this scene being told? If you got that down and really focus on the individual scenes instead of the bigger picture of the chapter, you'll find yourself writing more about that scene and therefore making it less rushed.
As for how to know which scenes are separate from each other, that's easy too once you understand it. The obvious ones you already know: whenever there is a large time jump, location jump and/or POV switch. However, scene changes can take place within the same location, time and/or POV. For example, in the first chapter, all the candidates are brought to the castle. Even if the castle is close by, even if we are still in the same POV, even if we're only 5 minutes separated from the previous event, it is still a scene change. The way it is written handles it as if it's not, which is the reason it feels rushed. The first scene, with all the people gathered and the names being called out, it should be focussed on more intently.
For example; William zones out as the King talks, but not a few seconds later he explains everything again but this time William does listen. For someone who believes he is about to die it isn't likely he would zone out while the king explains what exactly will be happening. What would be more logical is for the king to explain everything in the first scene. William gets nervous, the crowd feels too tight, his hands start to sweat and the realization starts to dawn on him with each passing moment. He's praying that it's all a dream when he hears his name being called out. This scene could be a very good way to deepen the connection with the character. You could really get into the emotions of the character, what do they value most on life? Why is he so sure he was going to die? Why is he so afraid to die in the first place? This scene has a totally different meaning and importance than when they are brought to the castle. The chapter could end just there when his name was called out and it all is just over in his mind.
Then, when the next chapter and scene start we are in the castle. Although pretty, William can't admire it fully with the lump that remained in his throat. The king repeats once again what this Quest is, though this time with more detail and they continue from there.
I hope this explains clear enough what I mean with focussing on scenes.
Something else I wasn't too fond of what Eleanor. What I think you wanted to achieve with her was a strong, confident and sassy girl, but if I'm being honest all I saw was a bratty, spoiled princess who thinks she's better than everyone. If that's what you were going for then great, but I really disliked her from the start. A character like her is hard to write, and if done wrong, easy to dislike. Her thoughts sounded a little arrogant, too, in my opinion. There is a difference between a strong sassy girl and a witty young woman with strength. What I personally would do, if I were to write a character like her, is keep her quieter, more observing and not jumping at every occasion to make herself look better or special. When William runs to the kitchen, have her let him, and when he figures out it is the wrong way and accusing her of not stopping him sooner, have her say something along the lines of "You looked so sure, I wasn't about to shatter your ego from the beginning." Though, don't have her say it with a smug grin or tone, make it as if she was seriously concerned she would hurt him like that when she says it, only to grin mischievously afterward. Personally, I believe that would make her a bit more interesting. She doesn't care if they win, so why wouldn't she play him a bit, have some fun herself? Those were only my thoughts on Eleanor, do whatever you want with it, it's still your story ;)
Little side note; I was a bit confused at the beginning. So, William and all the other people are poor and food is scarce and so is money. And yet, William had enough to buy an extra third whole bread he gives to strangers, his mom (by the sound of it) occasionally bakes cookies and gives some of them to the neighbor without hesitation, but he still has to become king if he were to keep his family from starving. If you ask me, his family is pretty well off, and if his family was still starving, perhaps they should stop feeding strangers (as crude as it may sound). Just saying.
So yeah, those are most of the things I've noticed while reading this story. Do whatever you want with this review, but I sincerely hope you can find use in my commentary. The story certainly is an interesting concept to watch unfold, and I truly believe in the Author to make that happen. The base is there, the ideas and the imagination, it's all there. All the Author needs now is a bit more practice to make perfect, but honestly, don't we all? I'm sure this author will make it someday if they were dedicated enough and kept on practicing and writing. Writing is a skill of time and patience, practice and killing your darlings. If you keep that up I have no doubt in my mind you'll make it ;)
So keep writing and never give up!