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Yes, you get an email from XBL to the email address that you registered the account with.
Do you mean a "modded" xbox? XBL has routinely done a sweep over XBL to find modded consoles, if yours get flagged, it's goodbye XBL.
XBL stands for Xbox Live, and is Microsoft's online service that allows xbox users to play games online and download content from the marketplace.
Yes, at least on the XBL version.
The simple answer is No...
..Accept on XBL festival or other special weekends when they decide to reward their fellow XBL contributers.