This is a great course, and so far I have been able to find everything else mentioned here in Blender 2.93.
Indeed the rendering settings have been completely changed; for Cycles you now have only two options: faster or more accurate and you can find them in the Cycles Render Properties:
And for the shading of the hair, we now have a Principled Hair Shader, which @jlampel explains here:
https://cgcookie.com/tutorial/using-the-principled-hair-bsdf-in-blender-2-8