you won't be able to buy a psp with cfw on it. instead check out this Pandora battery and magic memory stick guide which will help you install cfw. http://www.pspmod.com/forums/psp-hardware-guides/28839-easy-use-pandoras-battery-guide.HTML
Custom firmware is needed to do it, and if custom firmware is installed on the PSP in use, a plugin can be installed.
Hacking the firmware depends on the PSP's motherboard, not the current firmware installed. If you're asking whether or not it can be made into a custom firmware, then the answer is yes, but all homebrew would have to be rewritten for it.
Get a pandoras battery and magic memory card...
It's not the firmware that matters, it's the motherboard. A hackable motherboard can have custom firmware installed no matter what version of the official firmware it uses. 'Unhackable' (at present) ones can't have custom firmware installed at all right now. All phat PSPs can be hacked, most slims can, but recent ones can't, and at present, PSP-3000's can't at all.
Get another battery. You should of had backup files on your PSP battery.
You must have custom firmware installed, or be using the Half-Byte Loader.
The answer is both no and yes. You do not need custom firmware installed to run UMD games. UMD games are the disc-type games that you buy at the store. You will, however, require a custom firmware installed on the psp to run backups which are copies of the UMD (disc-type) on your memory stick.
No.
Firmware refers to the system software of a hardware device. Custom firmware takes the place of normal firmware, often adding functionality aspects to the system.
Right now there isn't. If you want to get custom firmware for psp version 6.20 you need to downgrade to custom firmware using a Pandora battery.
Not sure. Why not downgrade?
Die