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

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

A bomb goes off.
Carnage.
One person, only a few feet away, survives! How can this be?

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?

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where's the father?

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

Trying to tease Birbal, Akbar gave him one gold coin and ask him to buy
* something for him to eat
* something for him to drink.
* something to feed the cows
* something to plant in the garden
and most important you need to buy only one thing.

What must Birbal buy to silence Akbar?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?