You can trade Pokémon between your original DS, your DS Lite and your DSi but only if they're Diamond, Pearl or Platinum Game Cards. You cannot trade between Gameboy Advanced games using a DS because there's no link port for it.
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You can trade between two DS but only with DS games, otherwise you'll have to migrate them but then you cant put them back on a GBA game anymore.
Trading between an DS and a DS lite is the same as between a DS and a DS. There is no difference.
migrate via ds or ds lite. then go to pal park to catch the ones you migrated
Every single ds, ds lite, dsi, and dsi XL comes with built in wifi. To get to it, you have to have a wifi compatible game, and there will be wifi settings somehwhere on the game. You have to edit the settings. But i cant help you there. :)