I first read the books in the chronological ordering when I was about five. And that, I think, makes a big difference, because to a five-year-old, The Magician's Nephew is a slog. I didn't understand what the Victorian era was, or why we were in the Victorian era, or why the characters used such odd slang, or what a hansom cab was, or any of the references Lewis was making to other genres of literature, or how the whole book is a clever fantasy spin on Genesis and original sin. Don't get me wrong; it's a great book, and I got a lot out of reading it at such a young age. There was imagery and symbolism that was so powerful I could feel exactly what it was meant to express, even if I missed the delicate web of references it spun. But it's not representative of the rest of the series. It doesn't set the tone for what's to come, and it's harder for younger readers to get through.
On the other hand, I absolutely loved The Lion, The Witch, and the Wardrobe. I was less bothered about the details of the real world, because the book seals itself off in the Professor's country estate, and the war that drives the Pevensie children there is more stage-setting. The Lion, The Witch, and the Wardrobe sets the tone for the series much better than The Magician's Nephew. It's a lighthearted adventure with fun moments alongside its scary moments, heroes alongside its villains. The characters have agency and grow, and redemption, one of the major themes of the series, comes through much stronger.
So after I finished The Lion, The Witch, and the Wardrobe, I was eager for the next book and I picked up The Horse and His Boy. I was in for another shock, because even though the Pevensie siblings (in their adult forms) appear as minor characters, the main characters are completely unrelated to anyone we saw in either of the first two books, and the action takes place entirely outside Narnia. The tone is much closer to The Lion, The Witch, and the Wardrobe than to The Magician's Nephew, but it was still odd to think of the book as a sequel to either of them.
Then with Prince Caspian we're back with the Pevensies and it's a direct sequel to The Lion, The Witch, and the Wardrobe. And that continues with each of the last four books in the chronological ordering. Edmund and Lucy and Caspian himself reappear in Voyage of the Dawn Treader, then their cousin Eustace brings Jill Pole into Narnia in The Silver Chair, and Eustace and Jill come back to finish things off in The Last Battle. The tone is always fairly consistent, though The Last Battle reintroduces some of the cosmic tone of The Magician's Nephew, especially towards the end.
There's an obvious through line to The Lion, The Witch, and the Wardrobe; Prince Caspian; The Voyage of the Dawn Treader; The Silver Chair; and The Last Battle. Four of the five books have got a Pevensie in there somewhere (only The Silver Chair has no Pevensies at all). All of them have got at least one major character from the previous book. All of them have a tone of lighthearted adventure that gets heavier at certain moments. All of them have themes of redemption, and give their child heroes agency in the plot. Reading The Magician's Nephew before the other books muddles and confuses things. It shares some elements with them, but I found when I reread it later that a lot of it lands better if you already know Narnia. To take a very obvious example, there's a throwaway line on or near the last page that explains how the wardrobe from The Lion, The Witch, and the Wardrobe came to be. If you've read The Lion, The Witch, and the Wardrobe, that line causes a little thrill as you see the pieces come together. But the first time I read the book, all that line made me think was "What's a wardrobe?" That's always the way with prequels; they're written after the original, so they assume you understand the significance of certain things.
Now, to more directly answer the questions:
- Reading The Magician's Nephew first means that you understand exactly how Narnia was made from the beginning. But if you've never seen Narnia before, who cares how it was made? Reading The Lion, The Witch, and the Wardrobe and Prince Caspian first teaches you what Narnia is and why you should care about it. At that point, you're more interested to see what's in that world outside Narnia in The Horse and His Boy, The Voyage of the Dawn Treader, and The Silver Chair. And the beginning and end of Narnia that you see in The Magician's Nephew and The Last Battle have a lot more impact.
- The characters still develop naturally in the chronological order. Time in Narnia passes more quickly than in our world, so the children often show up hundreds of years after the last time they were there, and that means there are very few recurring characters. The Magician's Nephew and The Horse and His Boy aren't important to the development of any of the major characters, and the other five books are still in the same order relative to each other as the release order, so it's more like you get the same character arcs but they're interrupted by extra material in the chronological ordering.
- Some might prefer to read The Magician's Nephew before The Lion, The Witch, and the Wardrobe because it contains the allegory for original sin, while The Lion, The Witch, and the Wardrobe contains the allegory for Jesus dying on the cross. On the other hand, Aslan's sacrifice in The Lion, The Witch, and the Wardrobe is perfectly well motivated within that book, and if you understand the Biblical context enough to care about this, you probably already understand what original sin is. What allegory The Horse and His Boy has is more general and self-contained, and the other books are in the same relative order either way.
- Reading the five books that I think of as the "Pevensie arc" out of order could make things very confusing. These books do continue on from each other, and you'll miss important character development if you read them out of order. It's especially important to read The Last Battle last, because it really is the end of all things Narnia. You could read The Magician's Nephew and The Horse and His Boy pretty much anywhere and be fine, but I think they'll make more sense and land better if you read them after The Lion, The Witch, and the Wardrobe and Prince Caspian.
To wrap up, this is my preferred reading order for continuity of plot, character, theme, and tone.
- The Lion, The Witch, and the Wardrobe - It introduces the four Pevensies, who are pivotal characters in Narnia. It introduces the world of Narnia, and Aslan is a major presence instead of being on the outskirts like he is in a lot of the other books. The later books have lots of references back to it. Only sometimes are these vital to the plot, but it's still nice to get them.
- Prince Caspian - The direct sequel to The Lion, The Witch, and the Wardrobe, with the same cast of four Pevensies.
- The Horse and His Boy - The middle to end of Dawn Treader to me feels like the point where the series starts to get a little more mature, a little less lighthearted. The Horse and His Boy has the same lighthearted tone as the earlier books, so I recommend reading it here. Dawn Treader also wraps things up for the Pevensie siblings, so it makes sense to see them as kings and queens in The Horse and His Boy before then.
- The Voyage of the Dawn Treader - Introduces Eustace, the Pevensies' cousin, who will be important for the last few books. Wraps up Caspian's arc for the series.
- The Silver Chair - Eustace returns, along with Jill, who will be the main character for this one and The Last Battle. The Silver Chair continues the slightly darker tone that began in Dawn Treader.
- The Magician's Nephew - I think this is the right time to see how Narnia was made, once you care about it from reading the previous books. This book also has a darker tone, which will be less jarring if you've read The Silver Chair already. Otherwise it's pretty self-contained. Most of the characters are completely new. It's the first book to really dive into the weird cosmic multiverse stuff.
- The Last Battle - This needs to go last. It's basically Narnia's version of the Book of Revelation. Jill and Eustace return from The Silver Chair as main characters.