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1) The lost soul would go in the site, yes.
It was a ruling made awhile back that when the lost souls are exchanged, they occupy the exact same location as the soul they exchanged with.
It is in the REG under Instant Abilities -> Search, Reveal, or Exchange -> Special Conditions• If you exchange Ezekiel 34:6 (‘Wanderer’) with the Psalms 1:4 (‘Site Doubler’) Lost Soul that is in a site with another Lost Soul, the Ezekiel 34:6 (‘Wanderer’) remains in the site.