What is both possible and impossible at the same time?

What word begins and ends with an E, but has only one letter?

It can't be seen, can't be felt, can't be heard, and can't be smelt.
It lies behind stars and under hills, And empty holes it fills.
It comes first and follows after, Ends life, and kills laughter.
What is it?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

Why do you find that most of the buildings are deprived of the 13th floor?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

The peacock is a bird that does not lay eggs. How do they get baby peacocks?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

What does it mean?

Before Mount Everest was discovered, what was the highest mountain in the world?