In Pokémon, hidden abilities are special ability that Pokémon cannot regularly have through regular gameplay with the exception of the Hidden Grotto feature in Pokémon Black 2 and Pokémon White 2. Not all Pokémon will have hidden abilities but ones such as Pikachu like for example will have Lightning Rod as an example. Players would have been able to get hidden ability Pokémon from the discontinued Pokémon Dream World, the Hidden Grottoes as well as Pokémon X and Y's Friend Safari as well as X and Y's Horde Battles.
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You don't actually select when to use a hidden ability. Say your opponent tried to run from battle or tried to switch pokemon, the Arena Trap hidden ability would stop them automatically. (If you opponent is a flying type of has the hidden ability "Levitate" then the Arena Trap ability wouldn't work, but it works for all other type and abilities).
there is no hidden store.
hidden machine
It depends on the Pokemon your using.
Yes, unless stated otherwise. (As long as ____ is your active Pokemon)