I have been banned on my botting account but my question now is.. do I start a whole new account or do I just buy new keys and use the same battletag?
Depending on what the ban reason was, you can still appeal for the account to have the ban lift. Try filling the Ban Report Form and we will help you.
Depends on what you want. If it was just a botting account, I'd just make a new battletag, but they'll still know it's you from the IP unless you're using something to mask it. If it was your main that was banned, you can make another account under the same bnet and retain your mounts/pets/achievements.