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 went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?

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

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

They do not possess flesh or feathers or scales or bone
But still, they are blessed with fingers and thumbs of their own.

A cat had three kittens: Snophy, Topsy and Jorden. What was the mother's name?

Spot the cat in the picture below

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

Four cars come to a four-way stop, each coming from a different direction. They can’t decide who got there first, so they all go forward at the same time. All 4 cars go, but none crash into each other. How is this possible?