What is harder to catch the faster you run?

What Does this text mean:

important=important

Who is that with a neck and no head, two arms and no hands? What is it?

During which month do people sleep the least?

What can you hold in your right hand, but never in your left hand?

It is raining today at 11:59 am. What is the probability of sunny weather after 72 hours?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?