Q. Concerning solubility, how are the lipids classified?

Oils and Fats are hydrophobic molecules, i.e., they are insoluble in water and non polar. Lipids in general are molecules with a large non-polar extension and so they are soluble in non polar solvents, like ether, benzene and chloroform.

There are some amphipathic lipids, i.e., lipids whose molecules have a hydrophilic portion, like the phospholipids, giving them the property of being dragged by water, and a hydrophobic portion (non polar).