Also, Fawkes was close by on the night of Dumbledores death, We know that because he was singing.

So why didn't he help Dumbledore?

Fawkes has stepped in (or should I say flew in) just in time to save the day twice (2nd Book, 5th book) so why didn't he come and help Dumbledore if he was close by?
Because Dumbledore asked him not to save him, that's why. If not, Fawkes would have saved him.
It was all planned, I tell you!

Or what if Dumbledore was only injured by the curse, not killed and Fawkes was healing him? Do Pheonix's sing while they heal?
You know in the 5th book, Harry tries to do the Cruciatous curse on Bellatrix, but it only knocks her off her feet because Harry didn't desperately want to cause pain, he wouldn't have enjoyed it. So if Snape says the curse words without meaning it would it hurt Dumbledore? Probably not. Maybe it just knocked him off his feet, over the tower wall? Fawkes would be able to heal that.