You can call your service by using a button which calls a microflow. In the microflow you can use a call rest action – The documentation for it is here.
Hope this helps
I’m not exactly sure what you mean by ‘test your app from the homepage of your API.’
By homepage of your API, do you mean something like how do I test rest service you are PUBLISHING using the Swagger that is generated? Mendix publishes documentation of APIs you make for other apps to consume and you can test those from the swagger pages. Documentation on that can be found here:
Mendix also has a micro learning module on the academy page found here.
Alternatively, are you looking for a way to CONSUME REST services that other applications are exposing? If so, follow the link that Dragos provided. Hopefully this helps.