Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

Can you find out the remainder when 3^300 is divided by 5?

You measure my life in hours
I serve you by expiring
I vanish faster when I am thin
and slower when I am thick
The wind is my energy
What am I?

You have a 12 liters jug full of water. You have two empty 8 liters and 5 liters jug. How can you divide the water into two equal parts using these jugs?

The sum of a mother, her baby and her dog's weight is 170 Kg. How much does the baby weigh if the mother weighs 100 kg more than the combined weight of the baby and the dog, and the dog weighs 60 per cent less than the baby?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.