I look at you, you look at me, I raise my right, you raise your left. What am I?

What goes through cities and fields, but never moves?

French Police inspects a room where there are no windows, no doors, no tables and is almost empty expect there is just a puddle of water. They found a dead man who obviously hung herself from the ceiling, but they are not able to figure out how this had happened.

John and Jacob entered the crime scene and easily able to solve the case.

How did the man die?

In a jungle where there are no street lights or any other artificial source of lights, I notice a black snake crossing the road.
How did I get sight of the snake?

You can see three almost identical images below. Can you spot the odd one out from them?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

What will you call your mother's brother's brother-in-law?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

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.