What is full of holes but still holds water?

A murder has been committed in a house. You are a detective and have to find out the murderer.

You investigate by asking three questions to each of the six suspects. Out of those six suspects, four are liars. It is not necessary that they speak everything a lie. But in their answers, there must be at least one lie. One of the six is the murderer.

There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.

At the time of the murder, only the murderer was present in the killing room. Any number of people can be present in any of the other rooms at the same time.

Can you identify the murderer and the four liars? Also, can you find out who was in which room?

The responses of all the suspects are mentioned below.

Joseph:
Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.

Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
But I think that Joseph was in the living room, OH MY GOD!

Peter:
Mandy was in the kitchen with Christopher.
But I was in the bathroom.

David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.

Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.

PS: The corpse was found in the Living Room.

A father told his three sons he would die soon and he needed to decide which one of them to give his property to. He said, “Go to the market and buy something large enough to fill my bedroom, but small enough to fit in your pocket. From this, I will decide which of you is the wisest and worthy enough to inherit my land.” They all went to the market, and each came back with a different item. The father told his sons to come into his bedroom one at a time and try to fill up his bedroom with their items. The first son came in and put some pieces of cloth he bought and laid them across the room, but it barely covered the floor. The second son came in and laid some hay on the floor, but there was only enough to cover half the floor. The third son came in and showed his father what he bought. He wound up getting the property. What did the third son show his father?

The more of this there is, the less you see. What is it?

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.

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

Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar.
The villagers loved to talk of Birbal's wisdom and cleverness,
and the emperor loved to try to outsmart him.
One day Akbar (emperor) drew a line across the floor.
"Birbal," he ordered, "you must make this line shorter, but you cannot erase any bit of it."
Everyone present thought the emperor had finally outsmarted Birbal.
It was clearly an impossible task.
Yet within moments the emperor and everyone else present had to agree that Birbal had made the line shorter without erasing any of it.
How could this be?

What can you hold in your right hand, but never in your left hand?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

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