Good answers.
However, I asked all engineers from refraining to answer the questions.
Newtons Law of Viscosity only describes fluids that are considered "Newtonian," or fluids that are described in his law.
Common fluids such as gasses, water, Olive Oil, and mineral base oils are Newtonian.
Many other fluids are non-Newtonian and their viscosity depends on the rate of shear to which they are subjected. Greases, inks, and paints are considered non-Newtonian.
Some non-Newtonian fluids can change their viscosity with a change in both temperature and shear, and one of those is Viscosity Index Improvers (VII). However, shear-resistant VII's are the norm today. Shear resistant VII's means that even though some VII molecules may be sheared by mechanical forces, they can reform quickly.
Newton's Law of Viscosity is a Constitutive Equation and not a fundamental law of nature. In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied forces. I.E., it is not a fundamental law of nature but an approximation that holds in some materials and fails in others.