The FBI in the US has the physical instruments to harm citizens physically, that seems to give FBI the ground to break the constitution and intimidate all the 3 branches to take control of all the powers. How is that prevented?
The FBI falls under the purview of the Department of Justice, which is run by the US Attorney General. The Attorney General is nominated for appointment by the President, subject to approval by the US Senate.
So, the FBI is run by its director, who answers to the Attorney General, who answers to the President.
The Attorney General is subject to approval by the Senate. Like all Executive Branch functions, they are also subject to oversight by Congress, specifically the House and Senate Judiciary Committees. They must answer to Congress when called upon, and can be removed by Congress, even if the President does not want it to happen (impeachment).
Furthermore, funding for the FBI originates from and must be approved by Congress, who has sole spending authority.
If the FBI, itself, went rogue, the President has authority over the entire US military, subject to Congressional oversight. Army, Navy, Air Force, Marines, Coast Guard. Each state has their own militia under state control - the National Guard.
The federal marshal service is separate from the FBI, but within the Justice Department.
The ATF (Alcohol Tobacco and Firearms) Agency is also separate from the FBI but within the Justice Department.
The Secret Service, tasked with protecting the President from threats, is actually part of the Treasury Department (correction, WAS, per cpast - now in the Dept of Homeland Security), so separate from the FBI and even the Justice Department.
As you can see, there are plenty of armed military and law enforcement resources that could be called upon to counter and oppose the FBI if they decided to attempt some kind of armed insurrection.
Their very lawful authority that allows them to do so much of what might make them a threat would also be undermined by any such action, greatly reducing their chance for success.
The FBI is limited by the separation of powers. They are not immune to nor above the concept in action.