My only question is how much money is earned from every download of free games on itch.io, which I have been wondering for a long time.

How long is a piece of string? The answer varies from "zero" to "a decent amount", depending on the game. That's if I'm reading your question right, anyway. People do give money to free games, if that's what you're asking.

Itch.io isn't a site that pays developers for downloads.   Nor do people have to pay itch.io.

Itch.io shares in the revenue as per the individual game developers' settings.  However, itch.io carries over all the external costs to the individual user - like payment processing fees and tax certificates.  They carry the internal costs, the server, the admin, the software etc.  (or recover it from their revenue share).

If people voluntarily donate to the games or assets that are free, then the person who made the game or asset will get some money - else they won't.  There isn't any pattern there -some people will earn money, some will earn nothing. 

I know there are sites that pay game developers x amount per download, but they have a different business model, and claim that they receive the income out of external sites paying them for the data collection on the users, or for advertising and pass that onto the game developers.  But itch.io isn't one of those sites.