What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

A farmer and his neighbour once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbour, "and now he wants me to pay for the water."
"That"s right, your Majesty," said the neighbour. "I sold him the well but not the water!"?
The Emperor asked Birbal to settle the dispute. How did Birbal solve the dispute?

Rearrange the letters in "new door" to make one word.

A guard is positioned at the one side of the bridge saying ‘A’. His task is to shoot all those who try to leave from ‘A’ to the other side and say ‘B’. He also need to welcome the person who comes from another side ‘B’ to his side ‘A’. The guard comes out of his post every 1 hour and looks down the bridge for any people trying to leave. You are at side ‘A’ and wish to go to another side ‘B’. you also know that it would take 1:45 hr to cross the bridge. How will you cross the bridge?

The more you take me, the more you leave me behind.
Who Am I?

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

I am Huge on Sunday and Saturday.
I am small from Tuesday to Thursday.
I do not exist on Monday and Friday.
Who am I?

Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

What goes through cities and fields, but never moves?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?