Which hand does Link have the triforce on

It's definitely always been Farore. I haven't been able to find any definitive proof that it was ever spelled Fayore in any game. If it's possible that you misread it, then any number of other people could have, as well. This just happens to be a pretty big coincidence.

In the original Super Smash Bros. and Melee it's the Link from Ocarina of Time. In Brawl, they changed it to the Twilight Princess Link.

I figured this out by comparing the pictures of the Link from the Zelda games with his pictures from the SSB games. Ocarina of Time was only game out with that shield design when SSB64 and Melee came out. Twilight Princess has the same shield design, but Link's appearance in Brawl is basically identical to his in Twilight Princess. Also, that's what the Zelda Wikia says. :P

Zelda is also from Ocarina of Time in Melee and Twilight Princess in Brawl, since she also matches those looks.

Sheik is from Ocarina of Time in Melee, obviously since that the only game she's been in, however it is said that her Brawl appearance is based on conceptual designs for her in Twilight Princess.

It's claimed Ganondorf's Melee appearance is based of the SpaceWorld demo, although he looks a lot like he did in Ocarina of Time as well, and his Brawl appearance is again from Twilight Princess.