What occurs twice in a week, once in a year but never in a day?

I have one of the three numbers: 1, 2, or 3 in my mind. I speak only truth. You can ask me just one question for which I will only reply in yes or no or don't know. What question will you ask from me so that you are able to know the number?

I shave every day, but my beard stays the same. What am I?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

What is the Surname of Barbie Doll?

I travel all around the world but always stay in the corner. What am I?

The more of this there is, the less you see. What is it?

I was born in a small house and I live in it all alone. No windows and no doors have been assigned to my house. The only way I can go out is by breaking through the walls of my house.

Who am I?

A person was found dead on a big green land with no trees or buildings around. When the police arrived, they found a piece of rock lying next to him and the man was wearing clothes comprising of red, blue and yellow colours.

Can you tell who the person is and what was the cause of death?

An old Woman left INR 33,333 to be divided equally among two fathers and two sons and each was to receive INR 11,111.
How was this possible?