Circular table of death

Question: There are 1600 people sitting around a circular table. The first person (person 1) has a sword and kills the second person then hands it to the next alive person (in this case person 3). Person 3 stabs person 4 and gives the sword to person 5. This goes on until person 1499 kills person 1500. Then person 1 kills person 3 and so on. This is repeated until there is only a single person remaining.

Who remains in the end?

Question: Hard, Harder, and Hardest are brothers. By age from youngest to oldest, it goes Hard, Harder, Hardest. Hard is half the age of Hardest who is 20 which means hard is 10. Harder has a two-year difference between the number of years older he is than Hard and the number of years younger he is than Hardest. Harder is closer to the age of Hard than Hardest. How old is Harder?

Question: What gets broken without being held?

Question: You come across a Native American tribe and the leader wants to kill. He tells you, you can say your final words. If you tell the truth you will be burned at the stake. If you lie he will shoot you. What do you say to ensure survival?

Question: During what month do people sleep the least?

Question: Which eight-letter word still remains a word after removing each letter from it?