Hi
I'm a python/Django web application developer.
In order to be what you required, we will need to modify your site code, or build a system to sit inbetween the two sites.
API's work on the fact that one system or another has to ask for something. So the code has to work on the idea of 'A Thing happens and we perform an action'.
We cannot initiate actions from Intercom since its not yours, but we could either initiate actions in your site, or will have to build a third system to sit inbetween them.
This is based upon a quick review. We would need to discuss in more depth what connections you would like between the two systems
Thanks
Marc Nealer