Can you solve the photo plexer logic ?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Shyla was sleeping in her apartment when suddenly a robber broke into her house. He asked her to stay quiet and started looting the cash and jewelry. Suddenly the landline phone started ringing. The robber pointed a gun at Shyla and asked her to pick up and talk without giving away the situation.

She picked up the phone and it happened to be her husband. She spoke, Is it an emergency darling? Do give me a call when your flight lands, I will prepare your favorite food that will help you relieve the stress. Then she hanged up.

10 minutes after, the police arrive at the scene and catch the robber. How did the police know about the robbery?

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

Can you find out the remainder when 3^300 is divided by 5?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

There was a blind man. He had four socks in his drawer either black or white. He opened it and took out two socks. Now the probability that it was a pair of white socks is 1/2.

Can you find out the probability that he had taken out a pair of black socks ?

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

There was a greenhouse.
Inside the greenhouse, there is a white house.
Inside the white house, there is a red house.
Inside the red house, there are lots of babies.

What is It?

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?