Logic Riddles

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

What am I?

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

What am I?

Question: Using 3 periods (.) and 1 question mark (?) make this a logical and grammatically correct sentence:

"That that is is that that is not is not is that it it is"