4 Quad turrets for 16 Main guns, probably 50 calibers in length. Stated prior to be 16" guns. Of coarse since the fog have the Photon Canons, that gun size is enough.
If she needs a bigger gun she can easily deploy the Super-Graviton canon.
20 Double Barreled secondaries. I would assume they are the classic 5" gun. Probably closer to the 5" guns on modern ships. They have a sustained rate of fire of about 16-20 Rounds per minute automatic for the US designs. Other contemporary designs have ROF going over 60 rounds per minute on automatic.
Sounds like a CIWS, Close in Weapons System. Very high rate of fire. Either some gattling gun or a gun like the Bushmaster. Likely a crazy amount of turrets, probably 40-80 or so of the double barreled turrets.
On a Fog ship, VLS launch from where ever they want to.
Hanger that runs a good length of the ship, servicing all 3 runways. It sounds like two run along the side of the ship and are launch/land runways and a third runway that can launch aircraft going down the center of the ship.
Going to be an insane sized ship regardless. Probably a Length of over 1600 feet and a beam of almost 400 feet at the widest.
Just some estimated shots in the dark.