What goes through cities and fields, but never moves?

Consider this about a word: The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Five thieves looted a bank and they ran away in a car. The bank staff informed the police and they began the search of their car in their jeep. They found them on a road and chased them eventually catching them. The light that is used to fill the number plate was broken on the thieves' car. Also, the headlights of the jeep police were not working. How were the police able to catch the thieves then?

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

I have branches, but no fruit, trunk or leaves. What am I?

Can you move 2 matchsticks to form four equal sized squares.

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

What is the below Rebus indicate?