No, the Constitution says, "The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour, and shall, at stated Times, receive for their Services, a Compensation, which shall not be diminished during their Continuance in Office." in Article 3 and in Article 1 "The Congress shall have Power . . . ] To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof."

It could be said that Congress is mandated to pass a law defining Good Behavior, so that the judicial branch can execute its powers as defined in the constitution.

There has been debate on this actually. I can't find it because all search results are returning articles about current trust, but there was a period in history of very low trust in the court. This almost lead to some major changes, but they managed to rehabilitate their image by not being total villains. I want to say this was surrounding civil rights stuff, but I can't exactly recall.

They can be impeached by the legislature.