RE: Purpose of the atrium. With a vessel as large as the Enterprise, built for long voyages, it makes sense that a central core would exist around which officers and crew can navigate the ship. If your lost, go to the atrium core, and you can see which deck you want to get to, and navigate from there.
It also adds a sense of space, much like the lobby area of a large building.
It is always a good idea to have features such as this in a large complex to give a basic sense of geography beyond random corridors.
A starship could be traveling for a weeks or months at a time, and it's not good to have the crew feel confined.