Can you solve the photo plexer logic ?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

During an experiment, a guy throws a bouncy ball from a 100 feet tall building. The ball has a specific characteristic. Every time it hits the ground, it bounces up halfway.

How many bounces do you think the ball will make before it comes to a stop ?

There is a movie name hidden in the picture that is attached with this question. Can you find out which movie is it?

Can you solve below mathematical equation?

2^1234 - 2^1233

John has eleven friends. He has a bowl containing eleven apples. Now He wants to divide the eleven apples among his friends, in such a way that an apple should remain in his bowl.
How can He do it?

What is the word or phrase?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

I cry without having a voice.
I fly without having wings.
I bite without having teeth.
I whisper without a mouth.

Who am I?

What goes up but never comes down?