What is the Surname of Barbie Doll?

What does Alexander the Great and Winnie the Pooh have in common?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

Samuel was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a single hair on his head got wet. How could this happen?

Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?

Find the missing number in the image below.

What common phrase is represented by the below lines

Easy going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Medium going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Tough going:
Weak, 'I can't do it, I'm staying!'
Tough, 'Let's get going.'

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?