Joel is dead.
Ellie is hunting the Fireflies because they killed him (in retaliation for what happened in TLOU).
She's singing because Joel used to sing to her and music was a thing between them.
Quote me on it.
already had that theory
I assume it's that or in this post apocalyptic world ellie found love and her partner was killed by the fireflies and shes going for some revenge and joel isn't dead (or he died a long time before)