No, you can't. And even with a Pandora Battery, you cannot downgrade the 3000 or the late 2000 model.
Make or buy a pandoras battery
You cant yet, We will have to wait for it to come out maybe late this year We shouldn't have upgraded to 5.51
definitely no the best u can downgrade without a Pandora battery is 3.03.... what you can do is use the Pandora battery to downgrade and the results will be great I've done it on my psp and when i downgraded my psp i got to download as many games that can fit into my psp(full games of course) so downgrade your psp using a Pandora battery:)
It is impossible without the use of a Pandora Battery or Magic Memory stick.
The Pandora's Battery (PSP) is basically a hacked psp battery. when you put it into the psp it allows you to enter service mode. a feature which is used by sony and game developers to see if the games the have created work without buring it onto a UMD. it can also allow you to get CFW (Custom FirmWare) which is like OFW (Official FirmWare) but you can play backed psp games from your memory stick and run homebrew applications (Stuff made by psp users).
You're in luck! There seems to be a homebrew enabler out for official firmware 5.03. http://www.youtube.com/watch?v=lPMiNTbL7YQ
Get another battery. You should of had backup files on your PSP battery.
You can't, even with the battery.
Recently you can not make your psp with a custom firmware with out Pandora, Think about buying a Pandora battery on eBay, they are cheap.
Yes, you can if you have a 1000/hackable 2000. See http://pspslimhacks.com/easy-chickhen-custom-firmware-installer-without-pandora/
Without the latest official firmware, you can't access the PSN at all.
It has a built in browser. It should be on your psp if you are updated to the latest official firmware.