Did Davis not ignore his own constitution by failing to fill an entire branch of government that it called for?
Simple. A reading of the confederate constitution shows that like the United States Constitution it calls for three branches of Government: Legislative, Executive, and Judicial. Jefferson Davis never established a confederate supreme court as called for in Articel III. He ignored his own constitution.
Were people not locked up and newspapers not censored under his regime?
In his book "Southern Rights:Political Prisoners and the Myth of Confederate Constitutionalism" Mark E. Neely Jr. details many of the estimated 8000 political prisoners held by the confederacy during the Civil War. On a per capita basis those 8000 far exceed the 25,000 that Lincoln is supposed to have held. McPherson has several quotes in his book on the effects of censorship in Richmond.
Did the state not take control of whole industries like textile and salt, and exert undue control over others like shipping and railroads?
In his new book "Look Away: A History of the Confederate States of America" William C. Davis has a chapter titled 'Cotton Communism, Salt Socialism, Whiskey Welfare' where he goes into great detail on how the states took over and ran whole industries, allegedly for the war effort. One state, I believe it was Mississippi, had to import cotton cloth through the blockade for domestic use.
Enjoy.