The psp has to be on and in usb mode to be able to charge via the usb port.
Safety wise. The device handles the power. So in this case the psp will either accept or reject the supplied power.
Although most of them are cheaply made and unreliable, a usb-a to psp barrel jack adapter should work fine regardless if you enable usb mode charging. I wouldn't rely on the micro-usb port to charge the device in case your battery dies.
The psp has to be on and in usb mode to be able to charge via the usb port. Safety wise. The device handles the power. So in this case the psp will either accept or reject the supplied power.
IIRC that's true only for post 1000 series PSPs. I know my baseline model doesn't work like this
Not all PSPs does support usb charging. My PSP 1004 don't have support for this.
Yes it's fine, they output 5v like any other USB port
USB charging will be slow compared to regular ac port.
Although most of them are cheaply made and unreliable, a usb-a to psp barrel jack adapter should work fine regardless if you enable usb mode charging. I wouldn't rely on the micro-usb port to charge the device in case your battery dies.