Service Insight - is there a way to create Service using REST API?

There is an API endpoint to do this, since this is how the UI does it. However, that endpoint is available only in v3 of the API. You can deconstruct that API call (or series of calls, I haven't looked at it deep enough) and build your own to do it. You just need to specify v3 of the API instead of v2 or v1. 

V3 of the API isn't technically supported, so if you run into issues, support won't be able to help you. Contact your CSM and ask for v3 of the API to be published (supported and documented).