I make two people out of one. What am I?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

What do you see in the given picture?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

What can you serve, but never eat?