What does the below image rebus riddle means ?

Can you name some countries which do not have the alphabet 'A' in them?

I am written with two letters.
I said with the one.
I usually am seen with the two.

Who am I?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost?

What is more useful when it is broken?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

One night, a man runs away from home. He turns left and keeps running. After some time he turns left again and keeps running. Later, he turns left one more time and runs back home—but when he gets home, he finds a man in a mask. Who was the man in the mask?

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?