To me, part of the joy of Ico is how little they tell you. The game has a very “fairy-tale”-ish simplicity to it: there’s you (Ico), there’s Yorda (the Princess), there’s the (awesome-looking) Evil Queen, and there’s the shadows that want to take Yorda away. Your goal is simple enough: protect Yorda from the shadows while you both try to escape from the Queen’s castle.
I love how Yorda actually gets more accustomed to running around with you as the game progresses–how, at first, she’s really reluctant to make any big jumps when you motion for her to… but, as the game goes on, she actually stops hesitating, as if she’s coming to “trust” you. Late in the game, she even starts pulling herself up on ledges, without any assistance (BTW, wasn’t it a great moment when Ico jumps across the seperating halves of the bridge and Yorda catches him? I love that.) Yorda is exhibit A in demonstrating that, when done right, actions can speak just as loud as words when it comes to making you care about a character (considering that she doesn’t speak the same language as Ico).
As for your questions: we don’t know why the boys with horns are considered a bad omen. No indication is ever given, but it’s not really important anyway(and I’m pretty sure that guy in the intro was wearing a helmet with horns, but I could be wrong). Same deal with any “connection” Ico’s village might have with the Queen… I personally assumed that the kids with horns were the “tribute” she demanded from the villagers, and that they were too scared of her not to obey. And yes, the clear implication is that the shadows are what the previous horned children became after they were placed in those stone coffins–as you say, in the scene where you have to fight all the shadows at once, a coffin lights up for each one you beat. I thought that was a great, subtly spooky touch.
About Yorda on the island: like you said, we know that Yorda’s mother, the Queen, was planning on transferring both her mind and her power into her daughter’s body (presumably because her own body was almost completely “shadow-ified,” which I gather is bad). Notice that the parts of the Queen’s body that aren’t covered in roiling darkness actually look much like Yorda–white and translucent. After you kill the Queen (using a sword charged with her own power), I assumed that her power “defaulted” to Yorda, who couldn’t quite control it, and became a complete “shadow.” So she saved Ico and put him in the boat, but decided to stay behind in the crumbling castle so that her mother’s power would die with her.
However, either the power left her, or she somehow sealed it away, because she obviously got rid of it and decided to swim after Ico, luckily washing up on the same beach as his boat. We don’t know how, but that seems only fitting–after all, Ico is our PoV character, and there’s no way Yorda could tell him what happened (short of a long, involved game of Charades, I guess). I suppose it’s a testament to how much the game made me care about Yorda that I never really even thought to wonder how she survived–I was just glad that she did. Notice, however: Yorda’s different in that final scene than we’ve ever seen her–her skin doesn’t have that white “glow” anymore; it actually has some color. Maybe the power she had originally, and the power that came from her mother, cancelled each other out? Whatever the case, she’s definitely a normal human when you see her there. That’s my take on the situation, anyway.