Yes you can
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Yes if you have a Ps2 which can play both or, if you have a Ps1 you can only play the Ps1 game
no the game is not for a PS1
Yes the 80GB model will play select PS1 game titles
If it doesn't involve a joystick on the PS2, yes,yes you can.
yes, the ps1 controllers are dualshock, and the ps2 are dualshock2, so it may not be as good overall as a ps2 controller, but it should work