I know Nomura confirmed that the Mysterious Voice was Mickey and Felixx's explanation for why Mickey guided him is plausible, but I always thought it was Ventus from Birth by Sleep (This is spoilers if you didn't play BBS yet, so don't read this part if you don't want to get spoiled.) who was the disembodied voice. It just always seemed to make more sense to me considering it was newborn Sora's heart that was talking to Ven when he was in his fractured Station of Awakening when Vanitas was extracted from his heart. Not to mention, Ven has been residing in Sora's heart for about ten years since Sora was like 4-5 years old. He would've known Sora had the power to control the Keyblade just by residing within him. (Spoilers end)
As for Sora and Riku knowing about the outside worlds, the Keyblade War was considered to be a fairytale (which it's actually not) that was told to some people. While it's a bit farfetched for me to say this, there were probably people that lived to tell and pass down the tale to future generations, which explains why Kairi's grandma knows about the Keyblade War. If tales of the Keyblade War were passed down, why not stories about the outside worlds? Maybe Sora and Riku's relatives used to tell them stories about the outside worlds and Kairi only confirmed these stories when she washed up on the shores of Destiny Islands when Sora and Riku were young children. Not to mention, the islands they live on seem really tiny and the main island most likely doesn't have a very high population, so they probably know almost everyone on the islands. They've never seen Kairi before, so maybe their very much imaginative minds started to run wild and they instantly thought Kairi must have been from a different world. Which she is. As for why they absolutely had to leave, the answer is simple. Children, especially teenagers, are very adventurous. Sure, they love their home, but living on such a tiny, carefree island, I'm sure things would getting boring pretty fast. As for the reason why they knew to build rafts and sail through the sea to get to other worlds, Kairi did come to Destiny Islands via the sea (Kairi washing up on Destiny Islands is shown in the KH 1 Manga and not in the games. so I don't know if this is 100% true.)They probably just guessed that you could travel to other worlds through the sea. Those are my theories on the matter, so I could be very wrong.