The Home button is the same thing as the PS button. It's just more intuitive for PS3 owners, which are presumably a considerable percentage of the new consumers just now picking up a PSP.
Nobody knows if the Pandora's battery works with the 3000 models at this point, but if I had to bet on it, I'd say most likely not.
And 2000 models will probably be discounted come October when the 3000s hit retailers.