OK, I'm in stealth mode and I sneak behind the bounty hunter on the steps of The Friendly Arm Inn and I can't stab him. Does the Stealth turn into Backstab button or what? Can I do this or do they have to be hostile

First you have to use a melee weapon that a thief can use (like a long sword, dagger, quarter staff...). Then, hide in shadows, place your character behind the target (no need to be hostile), and simply attack. If you hit the target in one of the first 2 rolls (which is likely to happen, you get a -4 to THACO while hidden), it´ll be a backstabb (a message in the console will say so).

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http://www.angelfire.com/anime2/memnoch/ertai2.gif "Captive, captive... captive in heaven" -Ertai, Captive of the Blinding Angel