Yes you can. easily.
A family with a “duplex” declared house suddenly gets 10000 per year vs 5000. (just example numbers the real numbers will be higher based on history and gradual inflation)
The neat part is that it will all be legal, all out in the open, and local municipalities will have every incentive to allow such “residence splitting” because it means money for them.
Incorrect.
The prebate is based on the number of people in the house, not the number of houses. If you have a two adult house, the prebate for the adults is doubled. There will be no advantage to splitting the house into two houses each of which is headed by one parent. See:
http://www.fairtax.org/PDF/FairTaxPrebateExplained2007.pdf