Replace the question mark with the correct number in the below-given picture?

What is more useful when it is broken?

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

There are three identical triplets sisters. Demi is the oldest of them all and she always speaks the truth. Diana is the next one who is a liar always. Drew, the youngest of them all speaks both truth and lies randomly.

On a rainy day, a family friend Victor visited them. Since there were starkly identical, he was not able to recognize them. Thus to clarify, he asked one question to each one of them.

He started with the one standing on the left and asked, 'Which sister is in the middle of you three?' She answered, 'That's Demi.'

Then, he asked the one standing in the middle, 'What is your name?' She answered, 'I am Drew.'

Finally, he asked the one standing on the right, 'Who is standing in the middle?' She answered, 'She is Diana.'

Victor was left baffled. He asked the questions three times and received different answers every time.

Can you tell who was who?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

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?

Can you replace the question mark with the correct number?