That was the case throughout the 1980s and 1990s, after the Church Committee hearings in the 1970s caught them spying on Americans. But it's abundantly clear that President Bush tore down those walls, so we're back at square one.
The NSA absolutely spies internally. Even before the Snowden leaks it was already known that NSA trawling is how the Feds caught Governor Elliot Spitzer paying prostitutes.
And as far as I know there are no laws that prevent the NSA from spying internally. You're thinking of the CIA. The NSA is part of the Department of Defense, which is why it's always headed by a general.