Hi Barbora,
The sooner we all realize that AirBnB is like every other travel site, which is that they are only in it for the money, and learn to deal with things through that focus, the better things get. I made a few minor adjustments to our listings after I learned AirBnB was allowing people to do things which are illegal here. For instance, not counting infants in the guest total. License violation here. So I put it as a condition in my listing, and all guests have to agree to it.
If guests arrive and there are more people than the reservation states, I will correct the reservation accordingly. If the number in the group exceeds the license, they will be asked to leave. If they refuse, the police are called. I documented all of this through emails with AirBnB. They wanted to handle everything via telephone call, but I did not allow that.
I would recommend that you add a house rule that clearly states that the booker's profile picture is actually of them. If they do not, then you can deny them access when they arrive. Oh, and watch out for that thing where someone can book for someone else. I don't like that idea! The AirBnB platform was built on trust, and AirBnB keeps eroding things in favor of guests. That's where the money is, so I would expect nothing less.
All the best,
Jay