I'm consuming an API through "Consume REST API" and I'm able to successfuly test it in Service Studio.
It has one parameter, I fill values in the Test screen and get the resulting xml or json with the results.
But after publishing it , I get a "500 Internal Server Error" in runtime.
Can you give us more information on the error?How? In Service Center Monitoring > Errors
If you have the complete error just post it here (removing any personal data).
If not, activate the logs for that REST API and perform the request again. Then in Monitoring > Integrations you will have the complete request in order to try to understand what's wrong.
I'll wait for your feedback in order to help you.