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

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

Who has married many women but was never married?

A container contains 100 eggs. They can be either fresh or rotten. What is sure is the fact that there is at least one fresh egg in that container.

If you are asked to pick two eggs randomly from the container, at least one of them will be rotten.

Can you calculate how many eggs in that container are fresh?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

What does it mean?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?