What does does this rebus picture means ?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

There was a minor accident with a doctor's son but the doctor noticed no major injury. After the treatment, the father of that doctors son is sitting with the son of the doctor without the doctor being in the room.

How can this be possible?

You Throw The Outside, Cook The Inside
Eat The Outside, Throw The Inside.

What Is It?

You have a thousand Re. 1 coins with you. You have ten bags with you and you can put any number of coins in each of the bags. The condition is that if someone asks you for any amount between 1 and 1000, you must be able to give that amount by just giving the bag (you are not allowed to open the bag and give coins).

How will you do it?

Find three whole, positive numbers that have the same answer when multiplied together as when added together.

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?

Most people think of me as money. But when they find me in the water, they won’t get any money out of me. What am I?

A prisoner is told: "If you tell a lie, we will hang you and if you tell the truth, we will shoot you." What did the prisoner say to save himself?

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