Why Sapphira's egg appeared to Eragon. Bad/good luck. No, he was really the son of the one it was supposed to be sent to, and Arya was in a hurry. No, a hundred-ish Eldunari bent the magic to drop the egg off near Eragon!
I'm looking back at the series, and I deeply suspect that Christopher Paolini planned for the huge amount of WMG that Inheritance Cycle has generated. And he definitely left clues. He left so many for the Vault of Souls that people started assuming that the obvious answer was a feint. But Galbatorix's search for the True Name, on the other hand...
When a dragon dies, their rider lives on, but when a rider dies, so does their dragon. That is... honestly, extremely stupid. Dragon Riders were created to cement an alliance/treaty between elves and dragons, right? So including that in the spell that creates them is insanely incompetent, at best. But, remember, the spell was meant to end a war that - if I remember correctly( which I might not) - when on for generations. Obviously, the magician who put together the spell might not have been entirely down with the idea. Especially since they probably regarded dragons as mere animals.
A dragon doesn't necessarily die when their Rider dies.