What is more useful when it is broken?

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.

Find the smallest sentence with all the English alphabet.

What is the next number in this series?

4,12,84,3612....

What two things can you never eat for breakfast?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

Can you find out the remainder when 3^300 is divided by 5?

Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?

Six people park their car in an underground parking of a store. The store has six floors in all. Each one of them goes to a different floor. Simon stays in the lift for the longest. Sia gets out before Peter but after Tracy. The first one to get out is Harold. Debra leaves after Tracy who gets out on the third floor.

Can you find out who leaves the lift on which floor?