Are there parts of the ship that cannot be toured? Are you able to tour the gun turrets? The Bridge? Or engine room?

Yes. There are a lot areas that can't be toured. But, all you mentioned and then some can be toured. Bring water....it's hot inside and tons of stairs!

There are parts of the ship that are not on the public tour, but everything you name can be seen on the tour. Most of what is not on the tour includes additional examples of what is on the tour (the ship has four engine rooms, for example, but only one is on the public tour).

Yes

There are areas that are restricted but you will not feel like you missed anything. Examples of crew quarters are outfitted as if they were in use. There is a display of food in the mess hall as if a meal is being served. You'll see what it looked like when the ship was in operation. Highly recommended for anyone with am interest in military history. The below deck tour takes a while so take a bathroom break before you start.

You will get to access gun turrets, the bridge, and the engine room. Although there are restricted areas you will get a thorough tour. It's an amazing experience and cant all be soaked up in 1 day.