Technically, sweetbox is Western, but it's like they've switched on and off to Asian and they've always been Asian based... They've never sang a word of Japanese, but they've been signed by avex. With they're latest album they switched over to another label (I think), which is now actually an American based company. And also, they were formed in LA. So it's confusing, hah.
1. sweetbox is known in various parts of the world, but they're not huge anywhere, hah.

They don't chart well, and their albums are limited because of low sales. (Jade's solo albums are even worse with that. I can't find a regular online shop that has any in stock. >_<) It's a shame, I think both sweetbox and Jade herself are really good acts.
2. Yup. If they're popular anywhere, I'd say it's Japan, since that's where they mainly release. Though, they probably have a fairly big underground reputation with anime/video games geeks, because of the FFX-2 tie-in, hah.

And they may have a few fans from the Tina Harris era, when sweetbox was more about being Western.
3. I'm really not sure how many sweetbox albums have been released in the US, if any more than one, but the very first album was released in the US. I think maybe all the albums have been released in Europe, and I know many, if not all, are released in various Asian countries outside of Japan, such as Korea and Taiwan.
4. Jade was born in the US, and I think she might live there (LA?) now. But I remember hearing her staying in a European country before (was it Germany??--I forget ^^'), and she's probably at least stayed long periods of time in Japan, since that's where her records are mainly released, etc. Don't know much about Geo, though, sorry. I think he's foreign to the US, though...
5. I know for sure that Jade is at least very versed in Japanese, because she has spoken several sentences of it in various ads for albums and such. Again, not at all sure about Geo, though. ^.^'
6. I've never seen a sweetbox booklet, except for the LIVE album. It had English in it. So I can't help much here, but my best bet would be English, since they don't sing in Japanese. I'm actually going to order some sweetbox CDs in the next few months, so I'll get back to you on that.

7. It was avex not too long ago, but I believe Sony is their label on the latest album. Don't quote me on this, hah. They've had many labels support them throughout the history of sweetbox...
8. I'm not 100% sure, but I really doubt it. They're not THAT known, and I've never heard of such performances. But maybe I missed a rare one?
9. Again, not completely sure, but I don't believe so. I remember the latest album did pretty well for sweetbox, as I ~think~ it got into the top thirty. And I believe the best selling album is still Addicted (though maybe the last one passed it up?--can't find sales...), selling a little over 100k. So that should give you an estimate on how well they do on the charts.
10. This is the official site:
http://sweetbox.ning.com/
It's in various English AND Japanese, but I've never seen another site with just one or the other. They also have a MySpace:
http://www.myspace.com/sweetboxthenextgeneration
Which this is, of course, in English.
11. For the most part, I like the originals of the (miss)understood songs better. :X For example, I LOVE! Pride by Jade, but Ayumi's is meh. Ayu's Bold & Delicious is better, though, in my opinion.

For anybody who hasn't heard the originals, I highly recommend them.