A PSP 3000 skin won't work for a PSP 1000 due to some significant, though still minor, differences between the PSP 3000 and PSP 1000. The PSP 2000 and 3000 have a closer model shape so skins are more interchangeable between the 2000 and 3000.
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Yes, all the PSP chargers are the same. The PSP 3000's 5V charger works fine on a PSP 1000.
yes any psp charger fits into any psp
There is no such thing as a 'PSP 3000' game, no game is version specific like that. Any UMD game will work on the 1000, 2000 or 3000 without consideration of the specific version because they're all basically the same.
yes they can
of course you can! You can connect psp even with ps3