It seems like you might be looking at the King of Tokyo version of the cards, instead of the King of New York cards.
SheriffYes. You take no damage. The KoNY version has you dealing damage to buildings instead of gaining stars.
Sheriff Deputy. Temp. When you are instructed to lose hearts from paws, Win Star instead losing hearts.
Can I do this for every paw from the enemy attack?
Faster of the West. If I roll at least one paw, I dont receive damage at all? Yes. The English version is called "Fastest in the West" which is a play on "Fastest Gun in the West"
Short arm of the law. Your paws always damage your neighbours. Does this mean 'your paws also affect your neighbours? The word' always' confuses me. The KoNY version reads "Monsters in your Borough also lose [heart] from your [claw dice]."
Jurassic Roar. I unserstand this means that, when you use this Temp, your paws affect all enemies? The KoNY version reads "Play before resolving [skull]. You can move a Unit in your Borough to a different Borough."