You really need to know what type of API they are using. The methods you listed are programming methods for communicating with the API, but FileMaker is also a programming method for communicating. What does the API use specifically? Is it XML, JSON, or something else? Is it through http post, or GET, etc? Those are the details that are needed in figuring out the right path for FMP. Let us know what you find out.
Did you succeed in connecting FMP to the database of IB?