What is both possible and impossible at the same time?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

On 26-01-2022, Juli was murdered at her house in a city in India in the afternoon. There were three suspects in the murder and the following are the statements that were given by them:

John: I visited my village that day.
Jacob: I was out to deposit my house tax in the municipality office at that time.
Jonny: I was at a friend's place having lunch at that time.

Can you find out who is the murderer?

what one word does the below rebus identifies?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

In my garden, I have many trees but only one of them is the mango tree. In these mango trees, there are some mangoes(as expected).

But after a strong wind, there are neither mangoes on the tree nor on the ground. Explain?

What can jump higher than a building?