What does does this rebus picture means ?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

If Japan and Panama decided to merge into a single country, probably people will name it Japanama.

Can you think of two more such country's unions that could produce similar names like Japanama by overlapping their three letters?

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?

There are nine dots in the picture that has been attached with this question. Can you join all the dots by drawing four straight lines without picking up your pen?

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?