It is well known that covalent bonds, ionic, and metallic bonds are generally stronger than hydrogen bonds.

Then, why is that two notable hydrogen-bonded substances, as in ammonia and water, have much higher specific heats than mercury? That is, one would expect that the mercury's metallic bonds would hold more energy at a given temperature than other substances.

If degrees of freedom are involved, then why do multi-DOF systems such as covalently-bonded quartz crystals or salt crystals have specific heats less than water/ammonia?