Are bird statues the only way to save?
As far as I can tell, the bird statues are the only way to save. This article mentions save points in dungeons, and I am assuming they are refering to the bird statues as well.
There are save points scattered throughout the adventure, even in the middle of dungeons. This might sound like an obvious improvement, but it will be taken as something approaching heresy by the more traditionalist of Zelda fans. If you die, you can continue at the last save point with all of the items you've found. Nintendo clearly wants players of all skill levels to be able to finish the adventure.