The first three pictures are of the A138 1937 US BB Design XVI. The last preliminary design to USS North Carolina, she mounted 12-14inch/50 guns (3 x 4), 16-5"/38 (6 x 2, 4 x 1) on 35,000 tons with a speed of 27 knots.
The second three are of A137, US BB Design 1934 2, a 35,000 ton 30 knot battleship with 8-16"/45 (*4 x 2), 14-5"/38 (7 x 2) and adequate if not good protection.
The last three are of CC1933, a US Battle Cruiser design of 30,000 tons standard, 33,500 tons full load with a speed of 31.5 knots. Armament was to have been 9-14"/50 ( 3 x 3) and 12-5"/38 (6 x 2).
Complete details are contained in Norman Friedman's US Battleships of World War Two.
Bobby Weymouth