Sherlock Holmes Mystery Puzzles

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?

To attend world science seminar, A famous chemist from Russia visit
Tokyo(Japan). In the lab, the scientist was killed and his six assistants were under suspicion of killing the chemist.
Name of six assistants: Austin, Wayne, Dege, Oscaru, Lingard, and Rojo.
He left a note “76-20-44 79-16-22-7”

A local detective L Lawliet was called to solve the case,

After reading the note, L Lawliet instantly asked the police to arrest the murderers.

Who are the murderers?

Your an Intelligence agent and you are assigned to the case of a murder. A man named John was murdered by someone in the house. You are to interview everyone that was in the house on Sunday at 6:30 pm. You interview the kids first you ask them “what were you doing on Sunday at 6:30” the kids said we were playing with our toys. You interview the wife and you ask the same thing. The wife says she was cleaning the kids room because the maid said she was going out with friends. Next you ask the maid, the maid says she was getting the mail. Who murdered Mr. John?