What is more useful when it is broken?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

Bea Smith, Vera Bennett, Franky Doyle and Doreen Anderson were in Wentworth Prison for murder. But their behaviour in the jails is appreciated by the warden and the warden decided to give all these 4 prisoners 11 cupcakes. They all like cupcakes and they had all cupcakes in no matter of time but they do not know how many cupcakes each individual had. Therefore Bea started the conversation Bea: "Hey T-Vera, did you have more cupcakes than I had ?"Vera: "I do not know girl, Hey Franky, did you have more cupcakes than I had ?".Franky: "I do not know"Doreen replied instantly: "I know how exactly how many cupcakes each of you had?" So can you tell how many cupcakes each of them had?

Can you replace the question mark with the correct number in the below table sequence?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

A boy was locked in a room by some robbers. All that is in the room is a piano, a calendar, and a bed. The room is locked from the outside. What does he eat, drink, and how does he escape and get out?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?

What jumps when it walks and sits when it stands?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

I organized a small get together at my home.
In the party , i have a barrel with some whiskey in it.

Suddenly Guest 1 say 'I bet this barrel of whiskey is more than half full'.
'No, it's less than half full' Guest 2 replied.

I don't have any measuring instrument and without removing whiskey from it , how can i determine which of the guest is right ?