In general, they send the bill to the registered owner of the car. A
rental car agency sends them back the contact information of the persons
who had rented the car at the specified dates and times on the bill, and
new bills are sent to those persons.

Sometimes. In my experience, it's more common for the rental company
to pay the toll and then bill the customer.

So they don't make some staggeringly high charge for doing this (like they
would in Europe)

When I rented a car in Florida last year, I paid the rental car company and
it was about $3 plus the toll.

R's,
John