Yes, you can battle between different versions of Pokemon.
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the legendary Pokemon are different levels when you catch them. also in crystal there is a battle tower where when you beat it you can catch suicune without a masterball because you can battle him without him running away.
It is only possible to get Weedle in Pokemon Yellow by either trading it from Pokemon Red or Blue versions, or use the Mew Glitch and battle certain trainers.
yes,you can battle with any Pokemon game that's for the ds/dsi/the new 3DS.
You can't trade between every single version of Pokémon. You can trade between Pokémon Red, Blue, Yellow, Gold, Silver, Crystal and for the Japanese-only release of Pokémon Green. You can trade between Pokémon Ruby, Sapphire, FireRed, LeafGreen and Emerald. You can trade between Pokémon Diamond, Pearl, Platinum, HeartGold and SoulSilver. You can trade between Pokémon Black and White. in short, you can only trade and battle within generations. so black and white 2 will theoretically be able to trade/battle black and white. you can get pokemon across generations with pal park and poke transfer but you cannot trade over held items.
No. Pokemon Black and White have new Pokemon that the past games' engines cannot recognize. Even if you battle with Pokemon from previous generations, they might be loaded with moves from the new generation.