Can you solve below mathematical equation?

2^1234 - 2^1233

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?

I am never scared but became petrified and can’t live in a house but would die to make one. What am I?

I am quite hot but become too cold if you remove the first two letters. What am I?

Can you write down eight eights so that they add up to one thousand?

On a bright sunny day, two fathers took their son fishing in the lake. Each man and son were able to catch one fish. When they returned to their camp, there were only three fishes in the basket. What happened?

PS: None of the fish were eaten, lost, or thrown back.

Rose, Lily and Jasmine decided to buy flowers for their moms on Mother's Day. One of them bought lilies, the other roses, and the third one jasmines.
'It's funny!' said the girl with roses, 'we bought roses, jasmines and lilies, but none of us bought the flowers matching her name'.
'You're right!', said Lily.
What kind of flowers did each of the girls buy?

After a heavy Thanksgiving meal, the night watchman went to work. In the morning, he told his boss he had dreamed that a saboteur planted a bomb in the factory and that he felt it was a warning. The boss promptly fired him. Worker confused, Why boss fire him?

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?