Who told you soul and spirit are the same? The body is a temple for the spirit, together a living being is a soul. The outcome of salvation could be summarized as this: the saved live twice, die once; the unsaved live once, die twice, first is the death of the body, the second is the death of the soul.
As for Adam, my understanding is the "one day for a thousand years" equation, a day for the lord is a thousand years for mankind, Adamn died at 930, within 1000 years. I'm aware that in most sermons his disobedience is interpreted as "spiritual death", that's a sign of deviation from Sola Scriptura principle.