You will save 3 cards because the police has a rank of 3.
No. (if i dont really miss something)
The rank on the cards does not matter if you use them to bribe/bury/build/kill stuff.
From the rules:
"- You must play a number of cards defined by the
rank of the chosen card."
and from the kill part:
"Play on the table as many Guest cards from your
hand as the rank of the Traveler you just chose.
From the cards you just played, return cards with
the gun icon to your hand (these guests have an
aptitude for the Kill a Guest action); put the other
cards in the Exit Stack. (Exception: If you played
any Peasants, put them in the bistro of the inn,
instead of the Exit Stack). "