Can you identify if it's a murder or a suicide ?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

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

As you can see that fifteen matches have been used to form an arrangement. What you have to do is remove any six of them to make them ten.

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

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?

Find the combined weight of the Cat, Dog and Rabbit in the given picture.

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

What is the centre of gravity?

In case you were starting to feel confident, this one was meant for third graders in Vietnam. The answer is 66, but we don't blame you for scratching your head about how they got there.