I lived on Lamma Island (Yung Shue Wan) in 2013. I can't answer all your questions, but this was my experience...
Grocery shopping... Several shops sell fruits and vegetables at about the same prices as wet markets. Frozen meats and foods are also available if you cook at home. There are no chain grocery stores or pharmacies (that I saw in 2013). Anything I couldn't find on Lamma I just brought over and you'll see a lot of people doing this.
Restaurants... Local restaurants were (relatively) expensive. Western meals were really out of my budget. If it were possible, I would eat dinner elsewhere before taking the ferry home. But I'm somewhat cheap and was intentionally trying to save money.
Housing... My rent was $6k a month. I also saw a room with kitchen for $7k a month. I lived in the middle of a village where my window view was of the wall of the building next door. I'm sure that rent today is higher.
Transportation... The money I saved on rent ended up going to transportation. Taking the ferry every day cost a lot more than I expected, and the ferry rate is higher on weekends. I love taking ferries. The rocking of the sea is soothing to me and I would get a good 15 minute nap every morning. My commute to Central MTR was an hour (15 min from apartment to Yung Shue Wan pier, 30 min ferry ride with boarding and disembarking and 15 min walk to Central MTR). The downside is that after 8:30 PM, the ferry departs from Central every hour. There were a lot of evenings where I just missed the ferry and had to sit there for an hour waiting.
Internet... I encounted a few dead zones with my SmarTone 3G, but no more so than some random places in Hong Kong or Kowloon.
Outdoors and crowds... I spent less time outdoors on Lamma itself than I expected. At first, when the novelty was new, I was walking the town and family trail almost every day. Then the mosquitos really got to me (they even got into my apartment through the fan vents) as well as all the dog poop on the ground. There were also a lot of stray dogs and not all of them friendly. But I loved the (relatively) fresh air and went to the beach almost every weekend.
Conclusions... I wouldn't live on Lamma again. The money I had saved on rent just ended up being spent on the more expensive ferry transportation and more expensive local restaurants. It also quickly became rather inconvenient when making trips to Hong Kong/Kowloon because I was reliant on the ferry schedule. And I don't miss the mosquitos at all (though I had the same problem when I stayed in a village house in Yuen Long). There are definitely a lot of benefits of living on Lamma, but ultimately it depends on your lifestyle.