Understanding Nginx Rate Limiting Numbers

From my experiments it seems that per minutes is just a way to write rates that are on sub-second intervals. So 60r/m == 1r/s. This can be demonstrated by setting it to 60 requests per minute and then launching say 2 requests per second. It will be limited from the start, not only after 60 requests have been made.

That being said, I still don't fully understand how this all works :-)

503 Service unavailable is returned whenever you hit the limit requests. From the limitreq documentation:

If the rate of requests exceeds the rate configured for a zone, request processing is delayed such as that they are processed at a defined rate. Excessive requests are delayed until their number exceeds the defined number of bursts. When exceeded, the request is terminated with an error 503 (Service Temporarily Unavailable). By default, the number of bursts is equal to zero.

You did not specify a burst rate, so whenevery you do more than 5 requests per second, you will get HTTP 503 Service Unavailable in return. Try raising your limit or specify a higher burst rate.