How many sides does a circle have?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.

What is the total?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Where do fish keep their money?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?