3B. The Detect alignment spells do not automatically detect people based on their alignment. You have to have an aligned "aura". So, joe-blow Fighter who is Lawful Evil doesn't normally show up on a detect evil spell (unless he meets the exception of "evil intent"). But Lawful Evil cleric Mathias will ping on a detect evil spell even if he's thinking pure, good thoughts, or is sleeping. Certain creatures can also detect auras. I think Devils and Demons might have the ability to detect good auras (so they know who the holy guys are), but I'm not sure and don't have time to look it up.
This isn't true.
Anything has an aura if it has an alignment but normally it is too weak to show up under detect alignment spells until you get to 5th level at which point you radiate the appropriate faint auras of your alignment.
What the Aura class feature does for you is enhance your aura so it radiates stronger. There is a table under the spell here
Thus a 1st level fighter wouldn't radiate an aura but a 1st level warpriest would. At 5th level said fighter would have a faint aura and said warpriest would have a moderate aura.