Hammerspoon uses Lua for the configuration language. Phoenix uses JavaScript, or anything that translates to it. Personally I think Phoenix’s API is much simpler and easier to understand, but I’m of course bias. :) Hammerspoon does have some additional features that go beyond window and app management. Phoenix doesn’t cover those.
It looks like this just does window management, rather than the many things that Hammerspoon supports.
Yes! Though I’ve seen people extending the support in Phoenix cleverly by using the Task API. Basically you can run any external processes or scripts.