My impression is Neutral evil is someone who achieves evil in both systematic and random fashions, the method to which evil is performed is irrelevant to the Neutral evil. Chaotic Neutral is someone who lives on a whim and doesn't care for morality or law, he/she is a selfish individual. True Neutral is someone who is motivated by other means, a Druid for example always does whats best for nature regardless of how its achieved. True Neutral and Unaligned are different.

As for personality and Gods, I've always thought of it as a way of keeping a characters behavior consistent, a rough guide as to how a character should act in a given situation. As it impacts on their decisions it would impact on their opinions on the Gods too and as a result would find themselves drawn to particular gods.