Pandora batteries are no longer needed for anything on a PSP 1000. All CFW hacks can be permanently installed to the a 1000 via regular softmodding. Just follow the proper guides for your desired CFW and they will almost certainly have a section on how to make it permanent for your fat PSP.
As for adapters, if you want to use a dual one (I don't recommend them) then you have to ensure you use two identically sized cards or else it might malfunction. However considering what the prices are nowadays just buy a single 128gb SanDisk and it'll just work perfectly. Going up to 200 or above causes the XMB to slow down significantly, so I would highly recommend against it. I've also heard that crashes will happen more frequently if you try and use 512gb or more, the poor PSP just doesn't have the memory to handle giant file systems.