First of all, you're only going to pay the adults. That eliminates about a quarter of the population. Second of all, you're still going to collect taxes, so many people will just have the income taxed back. Say, only people below median income end up keeping the money. This cuts the figure down to 1.44 trillion. This is still a lot (we currently spend about $850 billion on social security, which would presumably be replaced by basic income), but it's not unmanageable.
Depends on how that income gets taxed. At a certain level of income, the gains of basic income are lost to extra taxation. However you always know that if you get fired you have a safety net, so it provides value to you even if you get 0$ net effect.
That is a rather trivial analysis that assumes a system where everyone, regardless of income, got $12k more than they would otherwise.
It would be easy to set a tax system such that people got $12k as a minimum, but those who earned (say) $20k received $6k and by $50k there was no increase. I'm not suggesting a curve with those figures, that is purely for an example.
[1]: http://en.reddit.com/r/basicincome/wiki/index
[2]: http://www.economonitor.com/dolanecon/2014/01/13/could-we-af...