Historically they launched with home-work travel, but as you mentioned, after a while people were short circuiting the system. On longer, occasional, travel there are much less chance that you will ride twice with the same person.
Here is a link to the UK site : https://www.blablacar.co.uk/faq/question/how-are-the-booking...
So the booking fee perceived by Blablacar is about 10% of the cost of the ride.
It is possible you used an earlier iteration or that different market have different prices. It is very possible booking is free in new markets.
In the beginning, you would pay the driver in person.
After a while, they added the option to pay on the site directly, with a fee (or perhaps without, I can't remember).
Lately (a few years ago, can't recall the exact moment), this is the only available payement option. You cannot book a trip without paying via credit card, at least in France.
Also, where is liability? Uber was fine until it started making a dent in established businesses. This hasn't yet but will get notice because of the headlines.