Yes, it works. PlayStation also has its own PC software for setting up this controller. The controller is therefore also suitable for use on the PC. As far as I know (not 100% sure), the profiles saved on the PC can also be used on the PS.

there is a program for pc
https://controller.dl.playstation.net/controller...

Yes, it also works on PC, but as far as I know you either need the DSX programme (can be downloaded from Steam) or you have to configure the controller via a console (PS5) beforehand to be able to use the paddles.

Unfortunately I can't answer this question as I only use it for the PS