1) The "Fair Tax" is the Flat Tax with a corporate focus group rebranding campaign, and nothing more. They are "completely different" the same way 'the death tax' and 'the estate tax' are.
2) Robert E. Hall and Alvin Rashbushka, "Low Tax, Simple Tax, Flat Tax" (McGraw-Hill, 1983), p. 58. A taste:
"It is anobvious mathematical law that lower taxes on the successful will have to be made up by higher taxes on average people."
Corporate tax reform is about allowing companies to repatriate profits into the US. Though some lobbyists will surely try to sneak gifts in for themselves, it isn't a conspiracy to reduce the tax burden on corporations, rather to exempt the US from the unintended consequences of dumb tax laws from a bygone era when American companies made virtually all of their money in the US.
Quoting economic regressives isn't particularly persuasive, either. It's a group of people who've staked their claim on the idea that economic functions can never be parabolic. Basically, they've never passed a semester of Calc I, but we'll roll their wheelchairs into the spotlight so they can flap their gums when it suits the flat earth perspective.