Unfortunately, you can't trade items through the PokeBank. This is simply because of the caution of piling up items into one game, which will be no challenge at all for the game.
As for your second question:
With this, you also have the ability to transfer content between various Pokémon X & Y games. It also has protections that prevent cheated Pokémon from being able to be transferred to the Bank.
If you read the bold parts, you would have read that you can transfer content between your copies of X and Y on the same console. :)
Hope I helped. :)
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