Logic Riddles

Question: Travel a mile and I will change.
Travel a million and I will end as I started.

What am I?

Question: You put me on a table and cut me, but you don't eat me.

What am I?

Question: There was once three trees. The first tree did whatever the third tree did, and the third tree did what ever the second one does. What happens if tree number two gets cut down?

Question: A woman is in the hospital for a routine procedure. The doctor leaves the room locking the door before he goes, the woman is alone. The doctor comes back to find the woman has died and there is another person is in the room. The door was still locked.
How is this possible?

Question: Before man discovered Mt. Everest, what was the tallest mountain in the world?