Can you find out which options fits best with the missing column?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

John bought 150 chocolates but he misplaced some of them. His Father asked him how many chocolates were misplaced.
He gave the following answer to him:
If you count in pairs, one remains
If you count in threes, two remain
If you count in fours, three remain
If you count in fives, four remain
If you count in sixes, five remain
If you count in sevens, no chocolate remains.

Can you analyze the statements and tell us how many chocolates were lost?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

There are 3 apples in the basket and you take away 2. How many apples do you have now?

In a fruit store, there was a unique weighing machine that was made to weigh only cherries and strawberries as they were priced the same.

Other fruits like watermelons or mango had different machines as they were expensive.

A man successfully buys watermelons at the price of cherries. How?

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

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

One day, Birbal got late for a function and Akbar was highly disappointed.
Please forgive me Jahanpanah. I arrived late because my child was crying and I had to calm him down, explained Birbal.
Does it take this long to placate a child? questioned the emperor. I feel that you have no idea about how to raise a child. I order you to act like a child and I will act like your father to show you how you should have dealt with your child. Come on! Ask me all that he asked from you.
Father, I want a cow, said Birbal.
The emperor quickly ordered one of the servants to bring a cow to the kingdom.
I want to drink its milk, now, now, now! said Birbal, imitating the voice of his child.
Akbar asked his servants to milk the cow and give to Birbal.
The servants quickly milked the cow and offered the milk to Birbal. He sipped in a little and then gave the bowl to the emperor.
As Birbal put up the next demand that was put up by his child a few hours ago, the emperor was stunned and left the room.
What did Birbal say?

Solve the following series:
AZ, GT, MN, __, YB