Can you find a five letter word that is left with only two letters if one is removed?

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.

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

There is so small cabin inside a deep forest.
All the forest burned out to worst possible but the inside of the cabin is still the same.
However all the person inside the cabin die.

How come ?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

A journalist was investigating a sacred cult in the jungles of Africa when he was caught by one of the person. He was confined in a cave till the leader arrived. The leader told him that he need to tell him a statement. If he thinks the statement is true, then the journalist head will be chopped off. If he thinks that the statement is false, his head will be smashed with a hammer.

What statement did the journalist make to survive?

I go up and I go down.
I go up towards the beautiful sky and down toward the green ground.
I am present tense.
I am past tense too
Children love me.

Who Am I?

I am looking for a word that change both gender and number when i add the letter 'S'.

What Word am I Looking For ?

To attend world science seminar, A famous chemist from Mexico visit
London. In the lab, the scientist was killed and his six assistants were under suspicion of killing the chemist.
Name of six assistants: Austin, Wayne, Dege, Oscaru, Lingard, and Rojo.
He left a note "76-20-44 79-16-22-7"

A local detective Jack was called to solve the case,

After reading the note, Jack instantly asked the police to arrest the murderers.

Who are the murderers?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?