How can a man go eight days without sleep?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

Can you make four (4) nines (9) equal 100?

I taste better than I can smell. Who am I?

Create a number using only the digits 4,4,3,3,2,2,1 and 1. So i can only be eight digits. You have to make sure the ones are separated by one digit, the twos are separated by two digits the threes are separated with three digits and the fours are separated by four digits

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?

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?

A sundial has the fewest moving parts of any timepiece. Which has the most?

Client Dempsey living in one of the East Coast states of the U.S. was talking to Landon Donovan, who was living in the West Coast state of the U.S.

Dempsey: What time is it?
Donovan: Wow, It is the same time here.

How is this possible?