What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

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

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

In a chess board, the queen piece can move horizontally, vertically and diagonally freely. The picture represents the same.Can you place 8 queens on the board in a manner that none of the queens can attack each other?

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

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

What is so fragile that saying its name breaks it?

I am a number I am not an odd number I am higher than 90 I am not higher than 100 If you subtract me from 100, you get nothing. What number am I?

A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?