Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

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

1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going toward the river. Each monkey had 1 parrot in each hand. How many animals are going towards the river?

It belongs to you, but other people use it more than you do. What is it?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

The centre of the third figure is empty. What digit should fit inside?