Yes, Pokemon SoulSilver is a Nintendo DS game so it can be played on a Nintendo DS
Yes, Pokémon Platinum was created to be a Nintendo DS game so it can be played on all of the Nintendo DS systems which includes the original Nintendo DS, the Nintendo DS Lite, the Nintendo DSi, the Nintendo DSi XL, the Nintendo 3DS and the upcoming Nintendo 3DS XL.
Sadly, you are unable to, You will need to 'transer' the pokemon from the GBA game in the Nintendo DS fat/lite.
Trading between an DS and a DS lite is the same as between a DS and a DS. There is no difference.
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.
Pokemon Black & White, Heart-Gold & Soul-Silver, Pearl & Diamond are all compatible with the Nintendo DS, DS Lite, DSi, and possibly for the DS XL and 3DS.
Yes, some DS Lite games will be compatible with the Nintendo 3 DS.
No, the DS lite does not use a memory card at all.
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Gamestop
No, Pokemon Gold version will not work on the Nintendo DS. Pokemon Gold is a GameBoy Color game, and the Nintendo DS's GBA compatible slot only works with GBA (GameBoy Advanced) games. Even though the GBA system is compatible with Pokemon Gold, the GBA compatible slot in a Nintendo DS is not compatible with Pokemon Gold.
the Nintendo ds, Nintendo ds lite, Nintendo dsi and Nintendo dsi XL
Nintendo ds lite=£130 Nintendo ds=£60 Nintendo dsi=£180
The Nintendo DS Lite 5 in 1 Combo comes in Black,Pink,Silver and Blue
Yes, Pokemon SoulSilver is a Nintendo DS game so it can be played on a Nintendo DS
Yes, the DS lite can play GBA games with the second slot.
The 3DS does not have a slot-2, it cannot use any accessories developed for it such as the Guitar Hero addon or the DS lite rumble pack. Those are only compatible with the original DS and DS lite.