those are some good questions and im gonna add some.

why wont this work with a 4GB/ 32MB mem stick?

does anyone know how exactly this patches the battery?

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oh, oh! Pick me! I know! The 32MB wont work cuz it isn't a PRO duo. I spent forever trying to do it on a 32MB card till I desided to try my 2gb.

Well, from seeing it install i guess it replaces the serial or something.

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1) Possibly, but I wouldn't try it. Downgrade to 1.50.
2) I don't see why it should be stuck. I'll do some testing later.
3) It should be fine. As above, I'll do some testing.

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1. it might need a 1.5 \ cfw for all the required functionality, why not try it and find out
2. if it cant be used with the magic files on it it can be formatted back to being a normal memstick
3. with the idstorage not being generated properly it can stop things working, it maybe fixable with one of the idstorage changers around, have a look in to it.
since you have lumines i'd recommend using it as it will have less impact on the idstorage and it will give you a full 1.50 psp.

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Once you get to 1.50, can't you just upgrade to 2.00 then downgrade again?

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1)Yes
2)Yes - format it in the psp's xmb
3)This link shows you how to make a completely original ID storage backup

Hmm, I use my magic memory stick to store stuff. It works just fine....so far.

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I should think it's possible, but it is advisable to downgrade to 1.50 and then attempt the Pandora Battery creation procedure. This way, you're keeping to the authors explicit instructions, and you can take advantage of the 1.50's other kernel functions, which may be required by the creator. Besides, if you were not to follow the instructions, it is unlikely that people will give support if something were to go wrong.

Of course! Just re-format it using your PC's OS or the PSP's built in formatting function. Just make sure the partitions are restored.

It shouldn't do, no. The whole idea of Pandora is to 'revive' the PSP, and flashing a 1.50 subset is purely to enable the PSP to actually have something to boot. It's more-or-less necessary to do another firmware upgrade or downgrade following an unbrick.
The iDstorage is supposed to remain 'untouched', even by SCE employees, which is why the battery flashing does not touch the iDstorage, and nor does any other upgrade/downgrader (including official ones). It was never expected that the iDstorage would ever be modified, hence there is no support for it in Pandora or JigKick. Hence, bricks from corrupted iDstorage are currently unrecoverable.

There's a tiny flash inside the battery, much like the NAND inside the PSP (but smaller). The Pandora creator does some patching here-and-there on the battery's flash, a notable one being a serial number, as zzaz3 said.

**Quoted gramtical mistakes in bold.

One more question, what are the known differences between this and the official JigKick or whatever it was?