what does the below math rebus puzzle mean?

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?

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?

A doctor and a boy were fishing. The boy was the doctor’s son, but the doctor was not the boy’s father. Who was the doctor?

Seven Robbers robbed a bank and hide the coins in a lonely place.
They decide to divide the money equally the next morning. Two greedy robbers decided to cheat the others and reach the place at night. They equally divided the coins between them, one coin left. So they called another robber and then they decided to divide equally among the three. Sadly again one coin left. The same thing happened to the 4th 5th and the 6th robber.
However, when the 7th robber reached in the morning, they can divide the coins equally.

How many coins were there in total?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

A shepherd had 18 sheep, out of which, all but ten died.

Can you tell us how many sheep was he left with?

How can you spell "White of an egg" in one word?
Hint: I know you can spell coke, poke, and joke.

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?