'invece di' vs. 'invece che' vs. 'piuttosto di' vs. 'piuttosto che'

Question

Quoted from 'Pinocchio' by Collodi:

Fatto sta che i tre torsoli, invece di essere gettati fuori dalla finestra, vennero posati sull'angolo della tavola in ...

Please, explain why Collodi uses invece di rather than 'invece che' vs. 'piuttosto di' vs. 'piuttosto che' and clarify whether these expressions, in that context, are interchangeable or not.

Answer 1

Both pairs are interchangeable, that is

• invece di is equivalent to invece che (the former is more common, La grammatica italiana)
• piuttosto di is equivalent to piuttosto che (the latter is more common, while the former is mainly used in the phrases such as "Piuttosto di niente, è meglio piuttosto!" - "Better anything than nothing," Grande dizionario italiano)

Answer 2

I agree that the two forms are interchangeable.

Moreover, at least according to Google nGram, invece di was more common during Collodi's times compared to piuttosto che.

I would generally avoid the usage of piuttosto di altogether (aside from the specific example cited by @I.M. and possibly a few more).