What is both possible and impossible at the same time?

Identify The phrase in the picture.

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

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

Replace the question mark in the picture below.

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

The horse jumps over the king.
Strangely there is absolutely no scratch on him.

Can anyone explain, how is this possible?

I am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?