You can change the gamertag by simply paying for a gamertag change ($10). This can be done by following the directions
As far as changing the gender of your avatar you'll need to delete your current one and make a new one. The avatar itself isn't connected directly to the gamertag. You can simply change the avatar and make a new one keeping the same gamertag. That can be done
in the avatar editor on the Xbox 360 console or at this link here.
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