The speaker of "Ode to a Nightingale" fools himself into believing that the nightingale is immortal, or at least its song is. But this statement seems only to give him another excuse to complain about human mortality – a common complaint in Keats's poetry. The nightingale's song echoes through generations of history, from Ancient Greece to Biblical times through the present. Keats was maybe the most "romantic" (notice the small "r') of the British Romantic poets, and he might have agreed with the saying that you shouldn't trust anyone over thirty. It seems that the worst aspect of death is not that old people must die, but that young people must turn into old people who die. The poem seeks an escape from this cycle.
The speaker's desire to die alone in the forest is just rhetoric, the equivalent of a drunken person who gets carried away in the heat of the moment.
The speaker cannot integrate himself into the natural world because he is too afraid of the natural process of death.