Can you solve the photo plexer logic ?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

Prove that twice of ten is the same as twice of eleven.

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?

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

I throw two dice simultaneously.

What is the probability of getting a sum as 9 of the two numbers shown?

Can you place three balls such that the equation shown in the picture holds true?

In a fruit store, there was a unique weighing machine that was made to weigh only cherries and strawberries as they were priced the same.

Other fruits like watermelons or mango had different machines as they were expensive.

A man successfully buys watermelons at the price of cherries. How?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?