What types of words are these: madam, civic, eye, level?

They are palindromes; they read the same both ways.
A certain five letter word becomes shorter when you add two letters to it. What is the word?

Short.I can run but I can't walk, a mouth but I can't talk, a head but I can't think, a bed but I can't sleep. Who am I?

A river.

From the beginning of eternity
To the end of time and space
To the beginning of every end
And the end of every place.
What am I?

The letter 'e'.