What is the word or phrase?

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth, the other always lies and you don't know which is which.
What is the question you ask?

As shown in the picture below, we can see a boy hanging on the tree branch to save his life. There are various ways in which he can die like1. A snake hanging toward the right waiting to bite the boy.2. A roaring Lion near the tree.3. Two crocodiles are ready to attack if the boy reaches near water. The tree is chopped to some extent, so can fall as if he moves a lot. Can you give this boy an escape plan?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

There were five men at church, and it started raining while they were outside. The four that ran still got wet, but the one that was still stayed completely dry. Why did he stay dry?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. 'Does John lie?' The person replied with a yes.

Whom did I talk with, John or Jacob?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?