I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

Which is the rope you never skip with?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

People put me on the table and cut me but do not eat me. What am I?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

What do you answer even though it never asks you questions?

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?