Gregory Paul Sales, 17, of Bidston, used the name Ransom to make 11 hoax bomb threats between September 2014 and April 2015, Wirral Youth Court heard.
He also threatened to "slaughter" the family of an FBI agent in a series of phone calls.
Admitting 12 charges, he was given a year in a young offenders institution.
John Weate, defending, said Sales, who was 15 when the offences started, "got into this" through playing video game Call of Duty.
Judge Michael Abelson said: "It is almost as if fantasy and reality blended into each other."
Sales pleaded guilty to one charge of making a threat to kill and 11 of communicating false information.
He was told he was "very lucky" to be young enough to avoid extradition to America.
The court heard on 4 September 2014 he rang the Ottowa County Sheriff and said he was on the way to Coopersville High School with a bomb and an Uzi submachine gun.
Hannah Griffiths, prosecuting, said 19 police patrols were sent to the school and the 2,500 students were locked down for an hour.
On 22 December he rang the home of FBI agent Christian Zajac who was "alerted to the call by the sound of his wife and children screaming" after hearing the voicemail message, Judge Abelson said.
In the calls, which were listened to by people Sales had met online, he demanded $20,000 (Â£15,800) from the agent and said if the demands were not met he would "slaughter" his family.
Sales also made threats in Michigan against Hudsonville and Caledonia Community high schools, Michigan State and Western Michigan universities, WZZM 13 and Wood TV studios and Gerald R Ford International and Kalamazoo International airports.
He also threatened Shuttlesworth International Airport in Birmingham, Alabama, and made a further unspecified threat to the FBI.
Sales was arrested following an investigation by officers from the North West regional crime unit Titan and the FBI.
He was given a two-year Criminal Behaviour Order stating he must notify police of any current and future social media usernames and email addresses.
Sentencing the teenager, Judge Abelson said: "This was coordinated criminal activity orchestrated on a large scale. This is no game."
A teenager has admitted making a series of hoax bomb threats against US schools and airports which saw flights grounded and buildings evacuated.