I assume you are talking about using someone else’s service for you to explore some test frameworks. For most cases this would be according to the User Agreement of a service, rather than an administrator. I do not know them well enough to know if you breach the agreements if you automate against them, but it is typically those that regulate what you can and cannot do. That being said e2e automation behaves like a user so it should not be breach in the Agreement by just using the service.
Also I would strongly suggest you not to do any kind of performance testing to a live service as that can quickly turn into a DDoS kind of attack, which is illegal.
There are services out there specifically for testing against 30 Days of API Testing Day 5: Publicly Available APIs to Practice API Testing which is a much better alternative than a live service.
If my assumption is wrong there are some material on the “test in production” as a concept.