Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

John was so frustrated to be the suspect of being a sleeper terrorist that he shoot himself right between the eyes with a revolver in his toilet. The revolver and the bullets were accurate. Minutes later John walks out of the toilet unharmed.
How can this be possible?

What goes up but never comes down?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

In the given figure, you can see that four match sticks are used to form a square. Can you form five squares by using six matches?

Solve the equation by replacing the alphabet with numbers.

MOM + MOM + NO = BOOK=

What is the word or phrase?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

Can you identify the direction in which this bus is moving; left or right?

Hint: The bus is moving on the roads of London.

A hen, a dog, and a cat are stolen. Three suspects are arrested named Robin, Steve, and Tim. The police are sure that all of them stole one of the animals but they don't know who stole which animal.

Sherlock Holmes is appointed to identify and is provided with the following statements from the investigation.

Robin - Tim stole the hen
Steve - Tim stole the dog
Tim - Both Robin and Steve are lying. I neither stole a hen nor a dog.

Sherlock is somehow able to deduce that the man who stole the cat is telling a lie and the man who stole the hen is telling truth.

Can you help him find out who stole which animal?