Can you solve below mathematical equation?

2^1234 - 2^1233

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186

Now deciphering the way it has been coded, can you find out how September will be coded?

Your last good ping-pong ball fell into a narrow metal pipe embedded one foot deep in concrete.
How can you get it out undamaged, if all the tools you have are your tennis paddle, shoe laces, and plastic water bottle, which does not fit into the pipe?

We are a group of eight brothers. We consider the weak, yet we protect the king in every battle. If we move ahead, we never turn back. Who are we?

Name a key which is hardest to turn.

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?

A pond had 60 fish, out of which, all but 20 died.
How many fishes are now present in that pond?

You are driving down the road in your car on a wild, stormy night, when you pass by a bus stop and you see three people waiting for the bus

An old lady looks as if she is about to die.
An old friend who once saved your life.
The perfect partner you have been dreaming about.
Knowing that there can only be one passenger in your car, whom would you choose?