The US gov't doesn't have to answer for its crimes, obviously. For example, to achieve everlasting immunity they simply don't subscribe to the international court.
No, they cannot. Sovereign immunity is absolute. US citizens can only sue when granted permission.
As 30thElement noted, the Federal Tort Claims Act grants this permission to sue. But there is no such right, and it is within the Federal government's power to change its mind and repeal the statute.
What were you talking about then? "Suing" is always a civil action. Taking someone to court for a criminal act is called prosecution and can't be done by just anybody.
People need to realize that this kind of action is not O.K., and those responsible should be brought to justice.