More Valuable When Broken

What 5-letter word becomes shorter when you add two letters to it?

I am a word that becomes shorter when you add two letters to me. What am I?

A king has 1000 wine bottles, and he discovers that one is poisoned. He has 10 prisoners to help him identify the poisoned bottle. The poison takes effect exactly 24 hours after consumption. How can he identify the poisoned bottle in just one day?

I am a word. Remove my first letter, I remain the same. Remove my last letter, I remain the same. Remove my middle letter, and I remain the same. What word am I?

You have 12 identical-looking coins, but one is either slightly heavier or lighter than the others. You have a balance scale and can use it only three times. How do you identify the false coin?

Three light switches are outside a closed door. Inside the room are three light bulbs, each controlled by one switch. You can only enter the room once. How can you determine which switch controls which bulb?