Tricky situation we have here. Guess I'll throw in my ideas.
Can you feel a deflection bonus? Feel your stat bonuses?
Generally I say the numbers are purely system constructs, something required of the system to keep everyone (in RL) on the same page. Characters may have an idea of how good they are with a sword, or dodging such, but they can't put a number on it. Unlike magic, I don't think someone would notice a supernatural bonus. I think the evil attacker would notice that you're harder to hit far more than you would notice that it's easier to avoid.
Using smite evil to bypass alignment detection?
I would say no, but if someone was really wanting a creative use for this ability, and you're the type to promote player creativity over all else, then a "yes" would include the consequence of "The evil individual feels the bursting aura of good energy, he knows he's been found out. Evil guy gets a init roll.
Killing evil characters out of hand ok?
If you personally know the evil character's crimes (like the above Satan example) then striking them down is good. However, if you cannot prove to everyone else in a lawful/good/neutral society the crimes of the deceased than prepare to be punished like you were the evil murderer. You won't be the first pariah to take that road for the well being of the unsuspecting innocent masses.
You could kill Sarevok outright, but proving his treachery will not only dismantle ALL his plans, but also keep you from being hunted by the Flaming Fist for the rest of your life.