I travel all around the world but always stay in the corner. What am I?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

There is a family that live in a round house. The two parents go out for a movie and leave a babysitter to watch their son. They come back and the kid was not there. Some one kidnapped him. The maid said she was cleaning in a corner. The cook said he was making pizza. The babysitter said she was getting a board game. Who kidnapped him.

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

Consider this: Arnold Schwarzenegger has a big one. Michael J. Fox has a small one. Prince doesn’t have one. The Pope has one but never uses it. Bill Clinton has one and uses it all the time. What is it?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

Nine marbles are arranged in the image below. Can you slide two marbles to form a square?