Our stay as the cave house was without any problems. They responded immediately to our requests, and were flexible with both check-in and check-out. We were greeted by a nice guy named Spyros, and got a welcome gift.
Keep in mind that the road path to the cave is a bit narrow, so we had to walk the last 5 minutes from where the taxi wouldn't go any further. There is also a bus stop about 10 minutes from the place. But It was hard to get any information about the time schedule for the busses. Would recommend renting an ATV!
There are no mobile signal inside the house, however the included free wifi network worked flawlessly.