Sometimes I come into these words in texts, but can't understand, in which situations each of them can be used. What's the essential difference between them?
'Amid' is rarely used nowadays. The only case I can think of off the top of my head is the Christmas Carol See amid the winter's snow. I'd call it archiac. It's preserved as a 'fossil' in the word 'amidships' - which itself is pretty well archaic (used to refer to the middle of a ship) but is often used by sport commentators (in Br Eng) when a player is hit in a sensitive area.
'Amid' may sometimes be used in poetry.