Can you trade Pokemon from one DS to another?

Answer 1

Yes, you may trade Pokemon from one Nintendo DS to another. However, there are limited Pokemon games which allow you to trade over the DS's wireless link. You may trade between Diamond or Pearl (even from Diamond to Diamond and Pearl to Pearl) but these two games cannot trade to any other Pokemon versions.

There is a special exception where Pokemon Ranger has a link to Diamond/Pearl and it is rumoured that you can trade some Pokemon from Pokmon Ranger: Shadows of Almia (second version - yet to be released) to it.

The Mystery Dungeon games can link Pokemon but not trade. You can certainly export a copy of your team or individual members, but not necessarily trade. Therefore, these games are also not able to trade over the DS.

If you are playing a Pokemon GBA game, you will not be able to trade using the DS. It cannot support the GBA link cabe, nor can it establish a propper wireless network with any GBA Pokemon game in it. Thus, you may only trade Pokemon over a DS if you are trading to and from Diamond or Pearl.