Which number should replace the question mark?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'

What are the two numbers?

John is asked to stand behind Jacob and Jacob is asked to stand behind John. Both of them feel confused about it and don't know what to do?

But it is quite possible, do you know how?

One evening there was a murder in the home of a married couple, their son and daughter. One of these four people murdered one of the others. One of the members of the family witnessed the crime.

The other one helped the murderer.

These are the things we know for sure:

1. The witness and the one who helped the murderer were not of the same sex.

2. The oldest person and the witness were not of the same sex.

3. The youngest person and the victim were not of the same sex.

4. The one who helped the murderer was older than the victim.

5. The father was the oldest member of the family.

6. The murderer was not the youngest member of the family.

Who was the murderer?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?

Take one out and scratch my head, I am now black but once was red. What am I?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?