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.

What number comes next in this sequence:
7 8 5 5 3 4 4 _

I have an eye but still cannot see.

Who am I?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

why number 8549176320 is one of a kind?

You know three triplets: Frank John and Wayne (need to return your money). Frank always tells the truth while John and Wayne always lie. You meet one of them on the road and can ask him a three-word question.
Which question, will you ask?

You are a thief and you are being punished for your crime. People have tied your head down on a tree with a rope that has been anchored in the ground. A candle is burning below the rope which is slowly burning it away. Just below your head, a Lion has been left loose and is waiting for you to drop down on the ground so he can have you as his lunch.

You have to survive the scenario. How will you do it?

The horse jumps over the king.
Strangely there is absolutely no scratch on him.

Can anyone explain, how is this possible?