I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

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 hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

Solve the mathematical equation in the picture below.

John said, "If yesterday was tomorrow, today would be Friday."

When did John make this statement?

There is an ancient kingdom where every married woman keeps information regarding the fidelity of other men. However, what they don't know is the fidelity of their own husbands. Also, there is an ancient belief that they don't tell each other about the fidelity of their husbands.

On a certain day, the queen of the kingdom declares that she has identified at least one unfaithful man in the kingdom. She allows the wives to identify and gives them authority to kill their husbands if they are unfaithful at midnight.

How will the wives manage it?

John named his first son Alpha, second Beta, third Charlie and fourth Delta. What is the fifth son's name?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

What has many teeth, but cannot bite?