Well, the GBA cartridge does have power and ground pins on it, so as far as I can tell it will use 5 volts as long as the DS is on. I haven't really tested this myself, as I use my slot-2 Supercard all the time so it would be impractical for me to eject it. However, I know that ejecting a slot-1 card will improve the battery life of a slot-2 card by about an hour, so I'd assume the same is true for the opposite way.
DSOrganize sometimes corrupts my miniSD card as well, but certainly not to the point that it's unrecoverable. Running Chkdisk on my computer usually fixes everything. It doesn't happen all the time either, but I tend to be cautious when using DSOrganize nonetheless.
I've never used Beup, so I'm not sure what the problem is. It could just be the Wifi issue with new DS Lites. If this is the case, Beup would have to be recompiled with the new Wifi library to fix this, so getting a slot-2 card wouldn't do much good.
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