What is both possible and impossible at the same time?

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?

Different lights make me strange by changing me into different sizes. What am I?

What goes through cities and fields, but never moves?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?

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

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

How is the moon similar to a dollar?

Until it is measured, not known. Yet how you miss it when it has gone. What is it?