How much control over Federal Reserve does the US Government have?

[matcheek]

or in other words who does the head of FED report to?
and the second question:
is the Federal Reserve a private institution?

I'm going to be a bit naive here, have just read about how the FED has been brought to life and can hardly believe that it did manage to survive for almost a century(!)
Have already checked many sources but cannot get a definite answer.

 

[william the wie]

The Fed is a private bank incorporated in Delaware. It is owned by American banks, the president appoints the leadership and it is headquartered near the Lincoln memorial.