Am I correct that there is no API for Zorro?

So there is currently no way to call Zorro from another program (e.g R or Python)?

Zorro is an executable. It indeed has an API. You can even share memory with it from another process:
https://zorro-project.com/manual/en/engine.htm
https://zorro-project.com/manual/en/command.htm

Is there a way to specify the path to zorro.exe in the custom application? or do I have to make sure zorro.exe is in the same directory as custom application for the ZorroControl.dll to work.

Your app must specify the path not to Zorro.exe, but to the Zorrocontrol dll. Use loadlibrary for that.