Are fatty acids and glycerol lipids?
From IUPAC Goldbook:


  A loosely defined term for substances of biological origin that are
  soluble in nonpolar solvents. They consist of saponifiable lipids,
  such as glycerides (fats and oils) and phospholipids, as well as
  nonsaponifiable lipids, principally steroids.


That means that lipid does not mean any hydrophobic molecule.
Lipids can be amphipathic as you already know about fatty acids.

Glycerol is not a lipid; neither is it hydrophobic. Glycerol, if to be classified into one of biomolecular classes, it would be that of monosaccharides (in the form of sugar alcohol like sorbitol and xylitol).