Any PS2 wireless controller should be able to work on the PS1. A PS3 wireless controller will definitely not work on the PS2 and PS1, because they use Bluetooth as their wireless technology, whereas wireless PS2 controllers use 2.4GHz as wireless technology.
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
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
A Playstation controller will never work as good as a PS2 controller and you need to just buy a PS2 used controller for a few bucks
The PS2 controller is better when would you want to play with a controller that was not as good
Yes
no it doesn't
There are wireless PS2 controllers available for sale
PS1 controllers will work on a PS2. However, PS3 controllers will not work with a PS2.
If it doesn't involve a joystick on the PS2, yes,yes you can.
Yes you can
Yes, but not with games that use pressure sensitivity.
PS2 controllers break and can be replaced. The market is loaded with used working PS2 controllers that should be purchased if your controller is not working perfect.