I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

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 may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

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?

There is an ancient kingdom where every married woman keeps information regarding the fidelity of other men. However, what they don't know is the fidelity of their own husbands. Also, there is an ancient belief that they don't tell each other about the fidelity of their husbands.

On a certain day, the queen of the kingdom declares that she has identified at least one unfaithful man in the kingdom. She allows the wives to identify and gives them authority to kill their husbands if they are unfaithful at midnight.

How will the wives manage it?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

There is something which you can be arrested for attempting but not for successfully completing.

A boy purchased a book from a bookkeeper and gave him $100.
The cost of the book is $50 but the bookkeeper has no change, so he gets the change from the next shop and returns the boy his $50.

After some time the next shopkeeper came with the $100 note and told the bookkeeper that the note was a fraud, so he took the money back.

How much loss did the bookkeeper face?

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?

What does this simple rebus mean?