There was some blurb as to the rational of the design of the Enterprise (justifying it after the model was made, perhaps, or this is what they thought of when designing the ship - I'm not sure and I don't have the book with the background anywhere near me.)
Warp engines were kept separate from the main body due to radiation. Most Star Trek ships kept to this design. This did change later on (The Bird of Prey from the films) but for the TV series it was mostly adhered to. The saucer of a Federation ship was intended to detach, both to operate independently, and to allow atmospheric landing. ST:NG used this quite a few times, but the original series and the films also referenced this technology. It was not unique to the Federation, either: The Klingon ships were supposed to be able to detach the front and back of their ships, too, for similar reasons.
As to why there is an 'up': In battle you need to have a clear reference as to where an enemy ship is in relation to you. So, starboard twenty degrees would be twenty degrees from your axis to the right. But up or down? Well, Positive ten degrees would tell you that, wouldn't it? And you can only do this if you have a standard reference plane to work from. And if you're doing that, why not set gravity to that standard plane? As to points where artificial gravity might intersect: You'd get Lagrange points within your ship: Points of zero gravity. These have appeared in other films and series where they have explored such concepts before (I remember seeing it, but can't remember where...)
But the main reason why all these ships look so outlandish is so people can recognise them. You need to know which are the good guys and which are the bad, and you need to know which series or film you're watching just by seeing the ship designs. I guess they learned their lessons from the old B-movies: You could watch those and see the same ships used, and the same space battle scenes used time and again (Battle Beyond the Stars, Star Chaser, Star Crash... just to name a few).