Not sure if this is the best place to post this because it is siding a little on the technical side, but you guys are better at answering than some other subs. Anyways to clarify, what i mean by recoil sections is, on the gun there is a small vertical drop in the gun. Just after the green paint. Did the section in yellow recoil into the green section or did the whole thing recoil at once?
Little side question here, did the South Dakota class have the same main battery as the Iowa class?
This isn't my area of expertise, but as far as I'm aware, they did not. The gun barrels were constructed using a "built up" method. In such a method, barrels are constructed from a series of concentric metal tubes, which are shrunk onto each other. This method of construction made it difficult to construct barrels in separate sections - no comparable British gun used recoil sections. The green paint is used on the slide cylinder, which is the part in contact with the slide in the turret, while the yellow paint is on the chase and muzzle, the main part of the barrel. The vertical drop you notice is where one of the tubes from which the gun is made comes to an end - there's another one partway into the chase. As to your second question, the South Dakotas and North Carolinas used the 16in/45 cal gun. This used the same chamber design as the 16/50 cal Mark 7 on the Iowas, but had a slightly shorter barrel (720 in against 800 in). If you're referring to the 1920 South Dakota design, those were intended to use the 16/50 cal Mark 2, which was more bulky than the Mark 7.
Sources:
REACTIVATION OF 16-INCH THREE GUN TURRETS IN THE BATTLESHIPS Arthur Romano, http://dtic.mil/dtic/tr/fulltext/u2/a183947.pdf
Jane's Battleships of the 20th Century, Bernard Ireland, Collins-Janes, 1996