Sitefinity API can`t be executed from external application that is not sitefinity the API needs the configuration files from App_Data/Sitefinity/Configuration folder, sitefinity services in Sitefinity/Services folder, web.config, basically all sitefinity related files that execute the web services and communication with the database where the data is stored. I am not sure if you have sitefinity assemblies placed for example in console application or another C# project from where the API is executed.
The concrete approach is to create a web service that utilizes sitefinity API and executes it in sitefinity then sends the result to another application.
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Public Issue Tracking
system and vote to affect the priority of the items