Good Riddles

Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others is bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?

Question:

John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.

What is the least number of eggs he needs for this to be true?

Question: I'm in everybody but everybody still wants me.
I won't feed you but I'll feed the tree.

What am I?

Question: What is harder to catch the faster you run?

Question: A boy at a carnival went to a booth ran by a man who said "If I can write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agreed, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50.

How did the man win the bet?