What does below pictogram mean?

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

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

Sherlock breaks into a crime scene. The victim is the owner who is slumped dead on a chair and have a bullet hole in his head. A gun lies on the floor and a cassette recorder is found on the table. On pressing the play button, Sherlock hears the message 'I have committed sins in my life and now I offer my soul to the great Lord' and followed a gunshot Sherlock smiles and informed the police that's its a murder.

Why did he think so?

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I am double, I am single,
I am black blue and grey,
I am read from both ends,
And the same either way.

A man is found dead with a knife in his back When the investigation is done. A chair lays beside him and the forensic team finds moisture around the body.

If he committed suicide, how did he do it?

I speak without a mouth, and hear without ears. I have no-body, but I come alive with the wind. What am I?

Spot 5 differences in two Christmas tree below:

You have a 12 liters jug full of water. You have two empty 8 liters and 5 liters jug. How can you divide the water into two equal parts using these jugs?

What goes up but never comes down?