I just want to offer some minor corrections.
First, as Dr. Acula already said, Ellone is not Raine's biological daughter; Raine took her in after her parents were killed. If you recall well, Laguna lives in her old house while Ellone lives next door with Raine. Laguna even talks to a picture of her parents when she's with him, telling them she's been a good girl.
Also, Ellone does say later in game that Raine died after giving birth to her baby (Squall), but I don't think it was said implicitly in-game that she died at childbirth. She even says that Raine told her something along the lines of wishing Laguna was there, so she could show him their son. We're never told the exact cause of Raine's death, only that she passed away when Squall was still a baby. He and Ellone where then sent to Edea's orphanage.
On that note, Ellone did not meet Squall at the orphanage. The dream sequence in Esthar is set before Adel is defeated by Laguna and the resistance. Laguna rescues her, and he manages to safely send her back to Winhill, but he has to stay behind to fight Adel.
So the exact chronology goes something like that: Laguna and Raine get married, Esthar soldiers come to Winhill and kidnap Ellone, Laguna leaves to search for her (unaware that Raine is pregnant; Raine probably didn't know it either at that point), Laguna finally finds Ellone in Esthar and sends her back to Winhill while he stays behind to bring Adel down, Raine gives birth to Squall and dies sometime afterwards, Ellone and Squall are sent to the orphanage while Laguna is still in Esthar (either because they're still fighting Adel or he's just been made president).
As for Centra, the Lunar Cry that destroyed it was much before the birth of any of the characters. I don't recall the exact date, but the continent was already abandoned by the time the orphanage was built there. I don't recall if it's ever stated why Edea chose to set it up in such a remote location; probably has to do with the war and wanting to keep the childrens as far away from it to protect them.
Then the Gardens were built sometime after Edea received the sorceress power for a second time (from Ultimecia, this time; we know she had been a sorceress before that), and she sent Ellone on the ship with the White SeeDs for safety reasons related to her unique powers.
As to why the children ended up in different Gardens... Well, we know Zell was adopted by the Dincht in Balamb, so that's why he eventually enrolled in BG. I think Quistis states during the basketball court scene that she was also adopted, but it didn't work out with her family so she joined Garden; BG was probably the closest one to where the family lived. We can assume the same happened to Irvine and Selphie; Irvine might have gotten adopted by a couple in Galbadia, and Selphie by a couple in Trabia, and they joined GG and TG respectively for some reason. Squall and Seifer never got adopted, so when the orphanage had to close down due to Edea starting to fight Ultimecia from trying to possess her, they were sent to BG, probably because Cid was there and could continue to watch over them.
Oh, and another piece of evidence about Squall's parentage that is often neglected... I recall someone posting a picture a few months ago that showed Squall's face superimposed on Laguna's face to show they shared the same facial features. However, Laguna has dark brown/black hair, and, if I recall well, green eyes. Squall's hair is a lighter shade of brown and his eyes are blue-grey. Raine's hair was the same colour as his, and from what we saw of her in the ending FMV, her eyes were a light colour. It was a bit hard to see though because it was a nighttime scene. So it's safe to assume she also has the same eyecolour as Squall.