Swallowing the Golden Snitch
1. How could Dumbledore know they were his only remaining family? Was he not aware that Sirius was Harry's Godfather?
Dumbledore knows almost anything, and family relations are too easy for him, I assume. James's parents might have already died - maybe they were used to bait James into being a Death Eater, but all the same, even if Harry's other relations were alive besides the Dursleys, he can't go live with them. I think Dumbledore had already suspected how the ancient magic of Lily's sacrifice for Harry would work. Harry needs to be under a home where Lily's blood relatives live. Hence, the Dursleys. It could have been his grandparents but let's assume that they're dead, otherwise Dumbledore would have picked them instead. Dumbledore's compassionate; if he had a better choice than the Dursleys, he would have picked it.
Of course, Dumbledore knew who was Harry's Godfather. He would know what's been happening between the members of the secret society he founded, but still - Harry needed to live under the roof of a blood relative.
2. If he knew about Sirius, why didn't he leave Harry in his care as James and Lily wanted? Sirius had not attacked Peter at that point, so that can't be the reason.
I think my answer in the first question answers this too :P
As for that, I'm very curious to know why Hagrid had Sirius's motorbike. If he borrowed it just to give Harry to Dumbledore, Sirius would have justificated his case (you know, betraying Lily and James). But then again, how could Hagrid ride a motorbike so well? Unless he has tried it before. Maybe Sirius taught him and lent it to him even before the betrayal.
Originally Posted by lucca4
EDIT: Okay, Molly practically summarised everything. And WOAH, my post is a spider!