I thought that diamond were the hardest substance on earth... but my friend told me that they can break. Is this true?

They can break, or it wouldn't be possible to shape them, but it takes a huge amount of force. They don't melt in anything you are likely to be able to do to them at home.

Diamonds have planes of cleavage, which means they have angles in their crystalline structure while allows them to break. Any sharp blow can chip or crack a diamond. Most chips occur around the girdle, or outside edge, and are actually fairly common, especially in diamond rings