I have a general question regarding the setup for a "bot" in the Facebook Messenger Platform. If I understand the architecture right, I can create an App as a developer add the Messenger function and associate 1 Page with the Messenger function. Does this mean I need an app for each page ? Or could I crete a "bot backend" serving multiple / different pages from different users ?
Yes, you can have one robot serving multiple pages. You just have to set <token> for different pages in API call, here is setup for a page. From documentation:
Graph API requires Page access tokens to manage Facebook Pages. They are unique to each Page, admin and app and have an expiration time.