I am not entirely sure how the whole aircraft share thing works, but from what I understand here someone has bought a plane and is selling shares in the aircraft, "shareholders" pay a monthly fee to cover maintenance and then pay per hour of flying.
As for the finances, I think there are some differences to an aircraft rental business. I would never be exchanging any money with anyone. My friend would book and pay through the normal booking system and then I would cover the fuel and landing fees.