What jumps when it walks and sits when it stands?

I travel all around the world but always stay in the corner. What am I?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

A man is looking at a photograph of someone. His friend asks who it is. The man replies, “Brothers and sisters, I have none. But that man’s father is my father’s son.” Who was in the photograph?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

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?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

What work can one never finish?