Posting in the Newbie tank comes with the expectation that you have searched for answers already, read through the various FAQs and done some reading already. You may need to go to different sections of the forums to find the FAQ that best fits your question.
There are at least 2 very, very good battery write ups on this forum already.
2. There are mini Tamiya, large Tamiya, DEANs, mini DEANs and RC type connectors
3. No. Read the specs for the charger.
5. most likely the mini is smaller
6. Yes. No.