Splicers are mentally unbalanced by over use of ADAM, but they are still many of them that are perfectly capable of higher level functioning. The "non-splicer" people someone was talking about don't really exist. Those people are just more lucid splicers.
As for how Rapture survived the previous ten years since the first game, that's largely due to the influence of The Family, Lamb's cult. She uses a combination of indoctrination and the pheromone technology that Ryan used against you in the first game to keep The Family in line. You'll notice there's actually less inter-splicer fighting in the sequel than in the original. How far reaching her influence actually is over the whole of the city is left unclear, since you basically travel in a straight line toward her along the old public transit system with no detours at all.
I loved the fact that the lowest, and therefore oldest parts of Rapture were featured this time around. The dense architecture, designed to waste not an inch of space, compared to the indulgent openness of some areas in the first game helped to highlight the socially stratified (literal) underbelly of Ryan's supposed free market utopia. In particular I enjoyed one of the logs made by Fontaine where he said that Lamb had the scam right, she just messed it up by believing in it.
EVE is a refined chemical derived from ADAM that basically works like suped up calories that let you use the Plasmid powers.
RE: ADAM/Splicing addiction. Jack, the character in the first game, is immune to it by design. More specifically, he's immune to splicing dementia and the psychologically addicting properties of splicing. He was engineered from the ground up to be able to use more plasmids, and channel more EVE with no ill effect that any normal person could do. Delta might be suffering ill effects, but he's so whacked out of his head as a bid daddy, how would you tell? They don't lamp shade it quite as much in Bioshock 2, but your're just as much of a puppet this time around.
