There is 16 badges in Soul Silver, both 8 in kanto and jotho.
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16 badges. 8 from Jhoto and 8 from Kanto.
You can't delete badges unless you start a new game.
you can challenge them after you get the first 8 gym badges
You can access Cerulean Cave in SoulSilver after you get all 16 gym badges (Johto and Kanto).
You need Hm Rock Climb, you need to obtain all 16 gym badges.