What has to be broken before you can use it?

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.

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

When is the top of a mountain similar to a savings account?

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

I go up and I go down.
I go up towards the beautiful sky and down toward the green ground.
I am present tense.
I am past tense too
Children love me.

Who Am I?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

I am not alive, but I grow; I don't have lungs, but I need air; I don't have a mouth, but water kills me. What am I?