Can you solve below mathematical equation?

2^1234 - 2^1233

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

Which digit occurred maximum times between the number 1 and 1000?

On 26-01-2022, Juli was murdered at her house in a city in India in the afternoon. There were three suspects in the murder and the following are the statements that were given by them:

John: I visited my village that day.
Jacob: I was out to deposit my house tax in the municipality office at that time.
Jonny: I was at a friend's place having lunch at that time.

Can you find out who is the murderer?

What has lots of eyes, but can’t see?

There is something which is always coming but never arrives?

A Car is crossing a bridge 2 miles long. The bridge can only hold 10000 lbs, which is the exact weight of the car. The Car makes it half way across the bridge and stops. A bird lands on the car. Does the bridge collapse? Explain.

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?