Its just there for decorative reasons. However mashabiki used to believe that was the 4th part of the 'Tetraforce'(just the Triforce with a pembetatu in the middle space). Pretty sure it has been removed since Wind Waker because of this.
I don't know. Unless the trolls at Nintendo planned Skyward Sword that long ago, then the extra piece could be the Goddess.(It does have the bird pattern...