What is both possible and impossible at the same time?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

Who can jump higher than a Mountain?

What are the next two letters in the following series and why?
W A T N T L I T F S _ _

*Hint: Check Puzzle Title

A woman lives in a skyscraper thirty-six floors high and is served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

A father's child, a mother's child, yet no one's son.

Who am I?

In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?

What has to be broken before you can use it?

A man is lying dead in a field where no one is around. His head is split open and his legs are disfigured. Near to him, there is an unopened package. No living organism can be found anywhere at the crime scene.

How did he die?