Is it a concern that if I request too many records too quickly through /api/resources/stats, I might interfere with the working of the Operations Manager? If this is a concern, are there guidelines for limiting use of this API, e.g., maximum records per minute?
That depend on your deployment size and the number of objects you are already collecting. In my case I had to build in a 0.2 sec delay when updating properties for about 2000 VMs. Each VM had its own API update call. Without the delay I saw that not all VMs are updated as they should have been.
In vROps you can search for "suite api". This will take you to the "vRealize Operations Manager Suite API-<FQDN>". Here you'll find the API metrics. In here best keep an eye on the CPU and MEM metrics.