What is the Surname of Barbie Doll?

What breaks yet never falls, and what falls yet never breaks?

It is always ahead of me yet I can never see it. What is it?

Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

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.

Different lights make me strange by changing me into different sizes. What am I?

Count the number of triangles in the below picture?

Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?