What does this nginx error “rewrite or internal redirection cycle” mean?

It’s a strange one all right, though I’m going to bet the problem is with:

        try_files $uri $uri/ /index.html;

The problem here is that the second parameter here, $uri/, causes each of the files in your index directive to be tried in turn. If none are found, it then moves on to /index.html, which causes the same location block to be re-entered, and since it still doesn’t exist, you get an endless loop.

I would rewrite this as:

        try_files $uri $uri/ =404;

to return a 404 error if none of the index files you specified in the index directive exist.

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BTW, those requests you are seeing are Internet background noise. In particular, they are probes to determine whether your web server is an open proxy and can be abused to hide a malicious user’s origin when he goes to perform malicious activity. Your server isn’t an open proxy in this configuration, so you don’t really need to worry about it.