A couple of replacement battery questions..

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http://androidforums.com – First, here is the battery I'm considering replacing my factory battery with- 3250mAh Battery for Samsung Galaxy S3 i9300 T Mobile Samsung Galaxy S3 T999 | eBay Question 1- Will a 3250 mAH battery harm my phone? Question 2- I notice it says it's for a 'T-mobile Samsung Galaxy T999'. I have an AT&T phone, are there different batteries for different carriers? Question 3- Any suggestions for a different, better replacement batteries? Thank you. (General)