In Discourse, the word for "newsletter" is "digest". And it can be set up by users to email them weekly.
About the integrated calendar, you're right it doesn't have one integrated. I wonder if someone would develop a plugin[1] for it...
Edit: Actually, somebody already thought of this and there's already a plugin[2] for it. Here it is in action[3].
[1]: https://meta.discourse.org/category/extensibility/plugin
[2]: https://meta.discourse.org/t/discourse-topics-as-google-cale...