I've owned a Cooper 416 since 1989 and would be happy to answer your questions. To answer the original question: the hull is not completely cored, but I couldn't tell you exactly where it goes from cored to solid. The hull coring (at least in my boat) as I recall is Klegecell, while the deck and pilothouse are balsa cored. We do not have the inside steering station. The original owner (the boat is an '84) had previously owned pilothouses and in his opinion the inside steering station was useless. Due to the interior height and the placement of the forward windows you would need a fairly high interior helm seat in order to have any visibility. If I ever get a "real" autopilot, though, I'll set up a remote at what would have been the inside steering station.
Our boat performs pretty well considering its beam, although it is very sensitive to bottom growth.
As far as storage is concerned, it will depend on the boat. It seems that the factory (at least in the '84 time frame) was willing to make extensive changes to accommodate the buyer's wishes. I understand that normally the 416 had a pilot berth to port at the companionway. Instead I have a large portside cockpit locker, and then below a large hanging locker, a set of drawers roughly 20" wide from cabin sole to pilothouse windows, and then a 20" wide locker that was used for.... a clothes washer. We never used it and removed it, leaving a 36" x 30" x 18" space just waiting to be filled with something. Eating up some storage space is a 40 gallon water tank under the v-berth and a 30 gallon holding tank under the settee at the table. The main water tank and fuel tank are installed below the cabin sole against the hull.
I noticed in another thread someone mentioning that the 416 has a single spreader rig. As you can see in the photo, that's not the case on my boat.