Using a false name on facebook is against their ToS, is it not? There was a story within the last week about how violating ToS is arguably a felony in the US.

The story was actually from 2013, but yeah, the DOJ tries to pass that theory. Fortunately the Ninth and Fourth Circuits have already shown they won't play ball, but there are other courts.

...do they care? Is there a correlation between committing crimes and, for example, being on the no-fly-list? The TSA doesn't wait for a crime to interrogate you, send you back, download or bug your phone, and I'll eat my hat if they never planted child pornography on someone's phone to accuse them of a crime. If a CIA/NSA clerk once flagged you as a "person of interest" (and 3rd degree phone relationship with a criminal is enough), they'll find a good reason to accuse you.