This drama does not have season 1 and season 2, the drama production itself classified it as part 1 and part 2,…
I think I know why they did this. If "Part 1/2 or Season 1/2" are not included, some people might watch part 2 first without knowing, since they both aired in the same year. So I don't see the difference between part or season. In my opinion, it should be like this "Alchemy of Souls" as part 1 and "Alchemy of Souls Part 2: Light and Shadow" as part 2 to indicate which one should be watched first.
Seungcheon put his golden spoon in the pocket before the gardener and him got switched. After they got switched…
Actually he can remember his past if he uses his Golden spoon because he is not Hwang taeyong anymore, so if he uses his Golden spoon he would remember the times he lived as Seungchun and Hwang taeyong. But obviously, he didn't use the golden spoon.