What goes up but never comes down?

I am quite hot but become too cold if you remove the first two letters. What am I?

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

Which point will the car reach to go out?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

I have an eye but still cannot see.

Who am I?

A man was convicted of a minor offence in Akbar court. Akbar decided to give him a chance. He asked him to give a statement. If the statement is true, he will be killed by lions and if it is false, he will be killed by trampling of wild elephants.

The convicted person requested help from Birbal and since the crime was not a big one, Birbal decided to help him. Whatever Birbal suggested impressed Kabir and he let the convicted person go.

What did Birbal suggest to the person?

A maths symbol is hidden in the below Bar Graph. Can you decipher it?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?