Did the CSA Congress even issue a declaration of war on the United States of America?
Now that you mention it, no. And considering the confederate congress was in session and the decision to bombard Sumter into surrender was made several days before the actual attack then there is no reason why the Davis regime couldn't have gotten the approval of congress in the form of a declaration of war before leading the nation into the abyss. But abiding by constitutional restrictions or requirements was never a confederate strongpoint.