Is that sphere the AI core?
Yes
If it is, why is it connected through a cable that thin?
Are you talking about the cable at the back? Because it's freaking thick (3 meters thick of cable, think about it). You might be confused with the mechanical support it's mounted on.
And why is the memory bank that close, but separated by a glass wall so the connection has to go around?
The connection is already going around (the AI is jacked into the wall behind it). As for the glass, it's mostly for the cool factor and to not have a bland sphere bottom.
I can't think of a reason you would want it close, but not that close.
The AI is directly connected into the memory banks, that's why it's so close.
And if the core isn't the sphere, why have the sphere? what does it do?
It's the brain of the ship, the artificial intelligence's core (not to be confused with the ship's core). That evil looking sphere with the eye IS the AI, the data banks under it are just there to provide extra processing power and memory. If you absolutely want to look at it from a non-roleplaying and purely game play standpoint then doesn't do anything, it's purely decorative and is a complete waste of space (which I couldn't care less about).
Can a wall console do the same thing?
A wall console could be used to access the AI, it's not the same thing. This is the actual computer/artificial brain that controls the ship (from a rp standpoint), not an access terminal. Of course, I could just make the entire thing a console embedded into a wall, but that would be extremely dull.
You're really overthinking things, it's a futuristic AI in a futuristic ship in a blocky space simulator, real science limitations just don't apply here :p . Think of it this way: Hal got an upgrade.
@ltmauve