1) Define. As in, are we allowed to criticize the media? Yes. Technically, you still live in a nation that supports free speech. If you mean if it's justifiable then that depends on the comment. If I said "All New York media is racist because it's run by Jews!" I would generally have a comment with little to know justification. However, if I said "The coverage on the war on Afghanistan was, in my opinion, too extensive." and proceeded to give examples where it was unnecessarily extensive you would have a justifiable comment.
2) Democratic? In what way? The minute you put restrictions or guidlines on free speech it ceases to be free speech. The idea of 'restricted' speech destroys free speech the same way, I feel, a Department of Ethics in the government destroys democracy.