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

Why is a river so rich ?

Today is a very icy and cold morning in Newcastle. Mr Shearer, an office bus driver arrived to pick up the employees from the last stop. Shearer suddenly remembers that he needs to pick a newly joined 4miles to the north. Mr Shearer lost his direction compass, a few minutes later Shearer is able to figure that he is moving in the correct direction i.e. north. How did Shearer know that he is moving in the correct direction?

Without looking at a calendar, within a minute name, a boy's name using 5 consecutive 1st letters of 5 consecutive months

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

What Time Should the last watch show in the below figure?

There are three boxes of different sizes with three cupcakes inside each of the boxes in Christina's kitchen. At night her daughter wakes up and goes to the kitchen. She opens a box and eats all three cakes.

But in the morning Christina finds out that each box still had three cupcakes. How?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

There's a day, that comes around once a year.
To celebrate the man, you hold dear.
He gave you life, love and will pick you up if you fall.
When it comes to guys like him, He's the best of all.
Who is he?