What brings you down but never up?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

A Doctor always sneezes before the rain. Doctor sneezes, Will it rain?

Cristina was born in 1888. She just had her 30th birthday today how did that happen?

Why is the longest human nose just 11 inches?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?