What is the Surname of Barbie Doll?

In a concert, Christina is performing a dance show with her group.
At 10:00, she and her crew were dancing in an absolutely straight line. At that time Christina was standing in 4th position from both the front and back end of the row.

What was the size of her crew?

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

You are on a Boat in the mid of a river. You have two cigarettes with you. One of these two you have to light, how will you light the cigarette?

Spot the cat in the picture below

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Identify Me

Hint1: I am a god
Hint 2: I am a planet
Hint 3: measurer of heat

Rearrange the letters in "new door" to make one word.