What is the Surname of Barbie Doll?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

A cat had three kittens: Snophy, Topsy and Jorden. What was the mother's name?

John can place six large boxes or nine small boxes into a carton.

Can you find out in how many cartons can he place sixty-six boxes in total?

What do you see in the image below

What is the next number in this series?

4,12,84,3612....

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

I am green and found in the forest and have needles instead of leaves. What am I?
Hint 1: It can be used for Christmas decorations.
Hint 2: I have a strong, scent that is used in air fresheners.