No, there are different kinds.
The black one works on GBA SP and regular DS only.
The dark grey one works only on DS Lite
The pale grey one is for both models of DSi and both 3DS.
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Yes, you can. However, all options still require a charger: The DSi XL, 3DS and 3DS XL chargers are all the same and can charge a Nintendo DSi
no. you can only use authentic Nintendo DS lite charger
You can charge the Nintendo DS with a Game Boy Advance SP charger (& vice versa) if you have the original version of the DS, the 'Phat' version. Otherwise, the DS Lite, DSi, and 3DS all have their own unique chargers. Each one is different, so you'll need a separate charger for each. (unless you buy an unofficial charger with lots of ends)
Yes. It functions the same way as the original Nintendo DS.
Yes, they are But the psp-Go has its unique own charger and a regular psp charger will not fit into a psp-Go.