What does this mathematical rebus means ?

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

What Word am I Looking For ?

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

Akbar called Birbal and asked him to draw a line on the floor. He asked Birbal to make that line smaller without erasing it. Birbal smiled and did it before Akbar could blink his eyes.

How did he managed to do it?

what's the probability of getting a king or a queen from a pack of 52 cards?

Which is the smallest number that you can write using all the vowels exactly once?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

What is the unique property of the following words ?
* Revive
* Banana
* Grammar
* Voodoo
* Assess
* Potato
* Dresser
* Uneven

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?