What's the only room from which no one can enter or leave

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.

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

One night, a man runs away from home. He turns left and keeps running. After some time he turns left again and keeps running. Later, he turns left one more time and runs back home—but when he gets home, he finds a man in a mask. Who was the man in the mask?

Some friends went on a vacation to a resort. It was raining heavily and it kept raining for thirteen days.

When it rained in the morning, the afternoon was beautiful and when it rained in the afternoon, the day was blessed with a clear morning.

Overall, the friends experienced eleven nice mornings and twelve nice afternoons. Can you find out the number of days they spent on vacation?

You are playing as white and given four rooks to checkmate the black king in four moves with the following rules 1. You can place one rook every move and ensure the black king should be in check position.2. After four moves the black king should be in the checkmate position.

What is the fastest way to double your money?

I’m light as a feather, yet the strongest person can’t hold me for five minutes. What am I?

What is 3/7 chicken, 2/3 cat and 2/4 goat?

What English word has three consecutive double letters?