Newbie questions.

[bah]

My strongest advice would be DO NOT BUY MEMORY STICKS FROM EBAY UNDER ANY CIRCUMSTANCES. Go to a local store or at least a trusted online retailer.
Some people will say they bought one on ebay and it works ok, many will speak of problems. Even the ones that work correctly are normally fake.
To me, its not worth the hassle.

The PSX emulator for the PSP is the official sony one that has been hacked to run other games. There are several versions of it (new sony firmware updates often have an updated psx emulator in them which is then hacked), some games run better on one than the others. Some games run well, some not so well.
You need to be running a custom firmware to use the PSX emulator (pops).

To downgrade you need to find someone with a PSP that can already run homebrew to create the pandora battery/magic memory stick.

You can buy a datel 'tool' battery or hard-mod a battery by cutting than pin, but you still need the special files on the memory card.

No-one can legally give you those, a second PSP that can already run homebrew is needed because is can both decrypt sony's protections, and run homebrew code.
With both those things it can modify an official sony update file into a magic memory stick.

The guide you linked to was written badly or the author was rather confused. The steps are ok but it doesn't mention that you need a second PSP that is already running firmware 1.5 or a custom firmware to be able to do them.
The pandora's battery creator app will not run on a PSP that cannot run homebrew already.