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There is one chest, that you can open up, it's contents are "Midgar Parts". try to put it on the model of Midgar,when it gets put in, another chest unlocks, it's contents are also Midgar Parts, do the same with it another chest containing Midgar Parts opens up and so on, do until all the chests in the room are open, and then their parts are on the model Finally, the chest close to the stairs opens up, and you get a keycard 66.
Yuffie is really easy to find, but you have to be excactly correct, or you won't be able to get her.
Walk around any forest area, until you fight Yuffie, defeat her, she's real easy to beat. Then you go to this place, there is a save point, never go to it, Talk to Yuffie. when she goes wanna fight, Don't fight her, keep talking to her. at one point, say that you want her to stay with you "because she's so good", she really isn't, but say it anyways. Don't ask her name, just say let's go. She'll tell you her name, and come into your group. If you screw up in any way, she'll take some of your money.
Vincent is in the BASEMENT of SHINRA MANSION in NIBELHEIM. But before you can get to the room where Vincent is in, you have to open a safe, the combo, isn't at the top of my head, sorry bout that, but there is a lot of clues. When opening the safe, you fight a big guy, once you kill him, you get Odin materia, and a key. Once you get that, go down to the basement, and there is a side door, before where you go to find Sephiroth. Go in that door, and you should find Vincent, keep talking to him until he joins your party.