I can be cracked, made, told, and played. What am I?

Trying to tease Birbal, Akbar gave him one gold coin and ask him to buy
* something for him to eat
* something for him to drink.
* something to feed the cows
* something to plant in the garden
and most important you need to buy only one thing.

What must Birbal buy to silence Akbar?

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

There is a place where if I stand up straight, I will still be considered sideways.

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

I look at you, you look at me I raise my right, you raise your left. What am I?

By adding four matchsticks, can you divide the square shown in the picture into two equal parts?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.