What is both possible and impossible at the same time?

He does not have any heart but still, He manages to live.
If you kill him, you will eventually die but yet you kill him.
He cannot run, who is He?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

Can you convert the number zero(0) into a positive number using just one mathematical operator ?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

I have branches, but no fruit, trunk or leaves. What am I?

A dead body is found outside a multi-story multinational company. The case is reported and a homicide detective is called on the crime scene.

He looks at the body and then towards the building. From the position of the body, it is evident that the victim committed suicide. He goes to the first floor of the building and then walks in the direction of the dead body, opens the window and toss a coin in the air.

He goes to second floor and again repeats the process. He keeps doing this till he is done on all the floors. Then he returns back to the floor and tells his team that it is a murder.

How in heaven did he deduce that?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

You need to move three matchsticks to form three squares. Can you do it?