What is both possible and impossible at the same time?

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

What has a ring but no finger?

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

Can you find out the number that should replace the question mark with a valid reason?

Can anyone tell me a word in the English dictionary which has a silent 'z'?

Akbar summoned Birbal out of anger.
He told him that he will have to face death.
He asked him to make a statement and if the statement is true he will be buried alive and if the statement is false, he will be thrown at lions.
After hearing Birbal’s statement, Akbar could do nothing but smile.
He gave him 5 gold bars and let him go.

What did Birbal say?