What is the word or phrase?

What brings you down but never up?

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?

Rearrange the letters in "new door" to make one word.

John’s parents have three sons: Snap, Crackle, and what’s the name of the third son?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

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

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

The chance of Mr John winning the lottery is 10%. All participants lined up and Mr John is 4th in the row. The first three participants lose the lottery.

What is the chance of Mr John now?