Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

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?

In the given picture, you can find two letters missing. When two particular letters are placed in the missing spots, you get an eight-letter word while reading in the anti-clockwise direction. Can you find out the missing letters and the missing word eventually?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?

0 0 0 = 6
1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

You can use any mathematical symbols in the space provided to make all above algebraic expressions true.

It begins where the time ends.
Its second is an expression of surprise.
Its third is a question.
Its fourth is urinate.
It ends with a drink.

Which country it is?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

I am not a bull but I have horns.
I am not an ass but I have a pack saddle.
Wherever I go, I leave silver behind me.

Who am I?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?