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Professor Oak isn't 50, I think of it as an in-universe typo and he is 60.
The PCs' age in my headcanon is 10 + their debut generation, except for the Alola kids who have 11, and the SWSH ones who would take the 17 spot.
The youngest gym leaders would be Tate & Liza at 14, and Iris at 15 but...