In which way can I attempt my question and assignment about the Law of Demand and Derivation of the Demand curve?
With the caveat that I don't know what terms, book pages, etc your professor expects you to be using, here's my suggestion.
What you're trying to explain is why the demand curve has the shape that it does. And this goes back to your earlier question about income effect effect.
The income is one part of why the demand curve is shaped as it is. It basically says that if the price of the good goes up, the amount of income (or purchasing power) goes down.
The other thing that determines the shape of the demand curve is the substitution effect. This states that if the price of one good goes up, substitutes for that good become relatively cheaper and people want to buy the substitutes instead of the original product.
These two effects combined are called the price effect.