Your idea that "on" suggests that the book was vertical but on the floor and then fell to a horizontal position is incorrect. Under normal circumstances in order to say this, we would say
The book on the floor fell over.
Let's look at your examples:
The book fell on the floor.
This is the normal and common way to say that the book was in someone's hand or on a table and fell off, landing on the floor.
The book fell to the floor.
Not the most common way to say this. It sounds slightly snobby to me, like it's from a movie set in England a century ago. Of course, current day people in the UK also use words that I would describe this way, so they may still say this over there. I might use this if the book's trajectory was interrupted, though:
The book fell off the table, hit the chair, slid down the curtain, and fell to the floor.
The book fell onto the floor.
This means the same as the "to" case--it's just less common. It has a slightly different emphasis. It is slightly more specific about where the book ended up. It didn't go through the floor, but came to rest on top of it. In this case the distinction isn't meaningful, so this form would be unusual.
Now let's talk about this jumping boy:
The boy jumped on the floor.
This usually means the boy was already on the floor and is jumping up and down. But it could also mean he jumped from something else to the floor. It's pretty generic.
The boy jumped to the floor.
You could say this if the boy got on a floor in order to do something. Like if the floor was a stage and he jumped up to it. Or if we are all sitting up in the seats and he jumped down the floor. I mean, it's not really common but it could happen.
The boy jumped onto the floor.
This means pretty much the same as "The boy jumped to the floor." They are both kind of odd scenarios, but they do happen. Here you are again emphasizing that he came to rest ON TOP of the floor, which in some cases could work with a situation where the floor is elevated.