What is both possible and impossible at the same time?

I am the fastest animal but cannot climb the tree. What am I?

A river should be crossed by a father, a mother and their two sons and two daughters.
There are some rules that should be followed while crossing the river. There can be only two people in the raft while crossing. The daughters cannot be with their father unless there is the presence of the mother. The sons cannot be with their mothers unless the father is present. Unless the guard is on the board, the criminals cannot be with any of the family members. Only the adults like the father, the guard, and the mother knows to use the raft.

How will they cross the river?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

John named his first son Alpha, second Beta, third Charlie and fourth Delta. What is the fifth son's name?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

Where do fish keep their money?

The Federal bank of London is abducted by the robbers. The head of the robbers asked the cashier to empty their money vault to them and when suddenly cashier got a call from her father. To avoid any suspicion, the robber asked the cashier to pick the call and reply her father in the shortest manner possible.

The cashier told her father "Is there an emergency father, Call me when you are free and I will help you in your furnishing" and then the cashier hung up the phone.

After 10 minutes, police arrived at the crime scene.

How did the police know about the robbery?

Can you count the number of quadrilaterals in the picture below?

What is at the end of a rainbow?