Is it possible to say, have a web app communicate to a desktop app and vice versa via External Methods?
Not possible. Desktop Edition has “External Method” greyed out. Worse, I’m unable to use the code editor after creating an External Method in the Web Edition.
That’s not what External Methods are about. External Methods are for calling functions in external libraries (.dylib, .dll, .so).
Possible. Works in both Web and Desktop. You should study the docs: Declare.
What are trying to achieve?
Your desktop apps will execute locally on a PC or Mac. The web app will execute on a remote host. The easiest solution seems rather to communicate over the Internet.
Unless you execute the web app locally, of course.