I have four wings, but cannot fly, I never laugh and never cry; 
On the same spot I'm always found, toiling away with little 
sound. What am I?

A Windmill.

What loses a head in the morning,
but gains a head at night?

A pillow.

I'm sometimes white, 
Although sometimes I'm black. 
I take you there, 
But never bring you back. What am I? 

A hearse.

A certain large animal lives happily and thrives here on Earth. 
One day, every single one of these critters is wiped out by a 
mysterious disease which affects only this particular animal. 
There are none left anywhere on earth -- they are all gone. 
About a year or so later, they begin to reappear on Earth again. 
How can this be?

The animal is the Mule. Since all Mules are born sterile, you can only get a Mule by crossing a donkey with a horse. That is how the species is able to repopulate itself.

I am always hungry,
I must always be fed,
The finger I lick
Will soon turn red.

Fire.

You are walking through a field, and you find something to eat. 
It doesn't have bones, and it doesn't have meat. You pick it up 
and put it into your pocket. You take it home and put it on a 
shelf, but 3 day's later it walks away. What is it?

An Egg.

Take away my first letter; take away my second letter; take away 
all my letters, and I would remain the same. What am I?

A mailman.