Resurrection
Yes, "By the First Bright
Easter Day" is using music of "Hark the Herald Angels Sing"; it
is based on the Glorious Mysteries, not just on the Resurrection.
Triple Alleluia of Easter Vigil:
This is used just after Epistle of that Mass (Tridentine
rite), and is the 1st use of “Alleluia” since just before
Septuagesima.