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Re: Some questions about S3
"The greatest" is a very subjective thing. The Nexus is the newest (for the moment), and has the most up to date version of Android, but the GS3 (and the soon to be available HTC One, and other phones) offer a lot of features the Nexus doesn't.
4.1 is definitely an upgrade over 4.0, but 4.0 isn't really bad in any way. I would expect the T-Mobile S3 where you are to get upgraded to 4.1 (jelly bean) in the near future, but that's just guesswork. Yes, 4.2 is "better", but not in a number of mostly small ways, not in any really big way.
If you root (to install and new OS version, or "ROM" yourself), then yes, that voids the warranty. In the U.S., at least, it's legal. If you need warranty support after rooting, you can probably restore to the original OS first, so your carrier will never know. Exactly how you would root and install an new OS depends very much on the specific version of the phone you have. I'd suggest going to the S3 forums on AC and looking / asking there. In general, you won't lose anything stored on the SD card, but might lose things stored in internal memory.
You will lose your applications, contacts, etc., but you can easily reinstall your apps from the Google Play store, and if your contacts, calendar events, etc. are synced with Google you'll get those back automatically. Again, go read in the S3 forums, especially the rooting forum for your model of S3. (Different carriers have different versions, and it's very, very important you follow the procedure that's designed for your version of the phone. And, if you're going to install a new ROM (OS), that you use a ROM specifically intended for your phone.