Library testing strategy with communications

thank you for reading!

I have developed Java Integration SDK for communication with a REST API endpoint. I would like to get advise on testing strategy and execution.

Should the integration sdk and rest server be deployed in dockers and then client executing test calls, or test should to to running dev server? Or I should make a custom endpoint?

Are there any standard REST integration testing protocols?

Any advice on how to simulate timeout, latency, not reachable endpoint and retries?

Happy Friday guys!