Of course you could, the jack on both Sony PS1 and Sony PS2 are exactly the same, although it lowers the performance than if you were playing with a Sony PS2 controller which means that you can not actually use the controller because who wants a controller that does not work completely.
Used PS2 controllers are cheap and there are no good reasons to try and use a PS1 controller on your PS2 because it will not preform like a PS2 controller
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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
yes, but I found that not on all games some ps2 games require dual shock 2 controllers.
If it doesn't involve a joystick on the PS2, yes,yes you can.
Yes you can
the larger ps2 you can ...yes not the slim ps2