Once you've booked you should get the direct number of the host, and if that's not a mobile number you can ask for it, AirBnb will let it through. I'm fairly sure you can also reply to an SMS message from the host and it will be routed to them (via AirBnb).
PH - you can book a range of places through AirBnb, from hotels through serviced apartments, down to someone's spare room in their house. The standards are generally exactly what you would expect according to type, I wouldn't expect a spare room to be fire inspected, though AirBnb do require hosts to have smoke detectors, etc. For a hotel or guest house it's the same as if you turned up and booked on arrival. As for insurance, I would generally expect to be claiming on my own insurance if those things happened, and if not, claiming through AirBnb would probably be easier than direct against a foreign guest house.