If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

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?

One fine day, an intellectual man came to the emperor's court with the aim of testing Birbal's wittiness. In order to do this, he challenged Birbal to answer his question and hence prove that he was as intelligent and witty as he was said to be.
He asked Birbal, Do you want me to ask one difficult question or a hundred easy ones?
Since both Akbar and Birbal had had a tough day and were eager to leave, Birbal hastily told the intellectual to ask him a single difficult question.
Intellectual: OK. Tell me what came first into the world, the egg or the chicken?
Of course, the chicken, Birbal replied with a smile.
This time with a note of victory in his voice, the intellectual asked Birbal, How will you demonstrate that?
What did Birbal say?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?

How much will a 38° angle measure when looked at under a microscope that magnifies ten times?

How will you measure 15 minutes using two hourglasses of 7 minutes and 11 minutes respectively?

Prove that the below maths equation is true.

8 + 8 = 91

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?