What goes up but never comes down?

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

A sea diver is a real show-off. He showed everyone that he can hold his breath underwater for 15 minutes.

I went to the diver and told him that I can be underwater for double the time i.e 30 minutes.
He responded that he will give me 100$ if I would be able to do it. I won 100$.

What did I do?

How high do you have to count before you use the letter “a” in the English spelling of the whole number?

I throw two dice simultaneously.

What is the probability of getting a sum as 9 of the two numbers shown?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

You are mixing a mixture of cement and Sand with five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four-gallon bucket and a seven-gallon bucket and neither has graduation marks. Find a method to measure five gallons.

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?