It means state within a state. Origin of the term is in 1990s Turkey. Military, police and justice system were upholding national interests and acting independently from the government.
Deep State is a form of clandestine government made up of hidden or covert networks of power operating independently of a nation's political leadership, in pursuit of their own agenda and goals.
Not particularly. As they were in control of the state, their goals were considered the national interest. It may not have reflected the will of the population or government, but that's often the case with national interests.