We had a great time at Francesco's house. It is indeed pretty small but it was enough for us - we live in Paris so we're used to small spaces! And on Lipari, you're outside all the time. The house is super clean and cosy. The bed is very confortable. There's a small kitchen space: enough to cook pastas and salads. You can't really get into cooking elaborated meals.
The terrace is absolutely great. The view is awesome. We had breakfast and few meals outside, it was lovely.
Regarding distances, I would advice to rent a scooter or a car. The 15 minutes walk from the port is ok but on a daily basis, it's time consuming. We rented a scooter and it was both practical and fun to explore the island and navigate in the city.
Also, it might be good to know that there is a road fairly frequented just below the house. With the door and windows closed at night, it's perfectly fine (the traffic is low at night) but when you're on the terrace during the day, you do hear cars and scooters passing by.
We didn't get to meet Francesco but he was easily reachable and gave us lots of advices and tips to plan our trip, which was greatly appreciated. Arrangments for the keys were super easy and we were able to arrive and leave as we needed.
We loved Lipari and the islands and staying at Francesco's was a great option!