I agree: a "state of nature" leads to lives that are "nasty, brutish and short." How do we find legislators who are good stewards for the public trust and welfare. We subject public companies to transparency regulations, perhaps legislator would benefit from more transparency. I am not sure where to draw the line to prevent mob rule or other undesirable outcomes, but legislators manage enormous budgets. Arnold Kling looks at ways to reorganize to create tighter accountability in https://arnoldkling.substack.com/p/the-unbalance-of-power
That's not quite true either. State protection is neither necessary nor sufficient to consistently ensure safety for any particular person or their property. Obviously, there's a sweet spot.
Um, not that I know of. There probably are some, but very small. Depends on what you mean by area. When I spoke of "not necessary or sufficient", I thought I was careful to quantify that expression over individuals; sharing your original framing "no man's […]". Certainly some people may possess sufficient skill and will and influence and have few enough enemies to be safe for life without a state. And certainly some people possess such great weakness and incompetence and antipathy and have enough enemies that no state could protect them.
Maybe that's a nitpick on your phrasing but I am a licensed Picker of Nits (one who happens to be a minarchist, not an anarchist, for what it's worth.)